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Linear Elements (linear + element)
Selected AbstractsPlant functional group composition and large-scale species richness in European agricultural landscapesJOURNAL OF VEGETATION SCIENCE, Issue 1 2008Jaan Liira Abstract Question: Which are the plant functional groups responding most clearly to agricultural disturbances? Which are the relative roles of habitat availability, landscape configuration and agricultural land use intensity in affecting the functional composition and diversity of vascular plants in agricultural landscapes? Location: 25 agricultural landscape areas in seven European countries. Methods: We examined the plant species richness and abundance in 4 km × 4 km landscape study sites. The plant functional group classification was derived from the BIOLFLOR database. Factorial decomposition of functional groups was applied. Results: Natural habitat availability and low land use intensity supported the abundance and richness of perennials, sedges, pteridophytes and high nature quality indicator species. The abundance of clonal species, C and S strategists was also correlated with habitat area. An increasing density of field edges explained a decrease in richness of high nature quality species and an increase in richness of annual graminoids. Intensive agriculture enhanced the richness of annuals and low nature quality species. Conclusions: Habitat patch availability and habitat quality are the main drivers of functional group composition and plant species richness in European agricultural landscapes. Linear elements do not compensate for the loss of habitats, as they mostly support disturbance tolerant generalist species. In order to conserve vascular plant species diversity in agricultural landscapes, the protection and enlargement of existing patches of (semi-) natural habitats appears to be more effective than relying on the rescue effect of linear elements. This should be done in combination with appropriate agricultural management techniques to limit the effect of agrochemicals to the fields. [source] A variational multiscale model for the advection,diffusion,reaction equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2009Guillaume Houzeaux Abstract The variational multiscale (VMS) method sets a general framework for stabilization methods. By splitting the exact solution into coarse (grid) and fine (subgrid) scales, one can obtain a system of two equations for these unknowns. The grid scale equation is solved using the Galerkin method and contains an additional term involving the subgrid scale. At this stage, several options are usually considered to deal with the subgrid scale equation: this includes the choice of the space where the subgrid scale would be defined as well as the simplifications leading to compute the subgrid scale analytically or numerically. The present study proposes to develop a two-scale variational method for the advection,diffusion,reaction equation. On the one hand, a family of weak forms are obtained by integrating by parts a fraction of the advection term. On the other hand, the solution of the subgrid scale equation is found using the following. First, a two-scale variational method is applied to the one-dimensional problem. Then, a series of approximations are assumed to solve the subgrid space equation analytically. This allows to devise expressions for the ,stabilization parameter' ,, in the context of VMS (two-scale) method. The proposed method is equivalent to the traditional Green's method used in the literature to solve residual-free bubbles, although it offers another point of view, as the strong form of the subgrid scale equation is solved explicitly. In addition, the authors apply the methodology to high-order elements, namely quadratic and cubic elements. The proposed model consists in assuming that the subgrid scale vanishes also on interior nodes of the element and applying the strategy used for linear element in the segment between these interior nodes. The proposed scheme is compared with existing ones through the solution of a one-dimensional numerical example for linear, quadratic and cubic elements. In addition, the mesh convergence is checked for high-order elements through the solution of an exact solution in two dimensions. Copyright © 2008 John Wiley & Sons, Ltd. [source] Limit cycle computation for describing function approximable nonlinear systems with box-constrained parametric uncertaintiesINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 10 2005P. S. V. Nataraj Abstract We propose an algorithm to compute the limit cycle set of uncertain non-rational nonlinear systems with nonlinear parametric dependencies. The proposed algorithm computes the limit cycles for a wide class of uncertain nonlinear systems, where the transfer function of the linear element and describing function of the nonlinear element need to be only continuous with respect to the parameters and continuously differentiable with respect to the amplitude and frequency of periodic input signal. The proposed algorithm guarantees that the limit cycles are reliably computed to a prescribed accuracy, and that none of the actual limit cycle point is missed out irrespective of the tightness of the prescribed accuracy. Moreover, for a prescribed accuracy, the proposed algorithm computes all the limit cycles in a finite number of iterations, and an upper bound for this number is also computable. The algorithm is demonstrated on a challenging non-rational example with nonlinear parametric dependencies. Copyright © 2005 John Wiley & Sons, Ltd. [source] A new class of stabilized mesh-free finite elements for the approximation of the Stokes problemNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2004V. V. K. Srinivas Kumar Abstract Previously, we solved the Stokes problem using a new linear - constant stabilized mesh-free finite element based on linear Weighted Extended B - splines (WEB-splines) as shape functions for the velocity approximation and constant extended B-splines for the pressure (Kumar et al., 2002). In this article we derive another linear-constant element that uses the Haar wavelets for the pressure approximation and a quadratic - linear element that uses quadrilateral bubble functions for the enrichment of the velocity approximation space. The inf-sup condition or Ladyshenskaya-Babus,ka-Brezzi (LBB) condition is verified for both the elements. The main advantage of these new elements over standard finite elements is that they use regular grids instead of irregular partitions of domain, thus eliminating the difficult and time consuming pre-processing step. Convergence and condition number estimates are derived. Numerical experiments in two space dimensions confirm the theoretical predictions. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004. [source] Asymmetric dispersal and survival indicate population sources for grassland butterflies in agricultural landscapesECOGRAPHY, Issue 2 2007Erik Öckinger We tested the hypothesis that populations in small habitat fragments remaining in agricultural landscapes are maintained by repeated immigration, using three grassland butterflies (Aphantopus hyperantus, Coenonympha pamphilus and Maniola jurtina). Transect counts in 12 matched sets of semi-natural pastures, and linear habitat elements proximate and isolated from the pastures showed that population densities of M.,jurtina and C.,pamphilus were significantly higher in pastures and in linear habitats adjacent to these than in isolated linear elements. A mark-recapture study in a 2×2 km landscape indicated that individuals of all three species are able to reach even the isolated linear elements situated at least 1 km from the grasslands. For two of the species, A.,hyperantus and C.,pamphilus, analysis of the mark-recapture data revealed higher daily local survival rates in the semi-natural pastures and more individuals dispersing from pastures to linear habitat elements. The proportion of old compared to young individuals of C.,pamphilus and M.,jurtina were significantly higher in linear elements than in semi-natural pastures, which suggests that butterflies emerging in pastures subsequently dispersed to the linear elements. In combination, these results suggest that semi-natural pastures act as population sources, from which adult butterflies disperse to surrounding linear elements. Hence, preservation of the remaining fragments of semi-natural grassland is necessary to keep the present butterfly abundance in the surrounding agricultural landscape. [source] Higher-order XFEM for curved strong and weak discontinuitiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2010Kwok Wah Cheng Abstract The extended finite element method (XFEM) enables the accurate approximation of solutions with jumps or kinks within elements. Optimal convergence rates have frequently been achieved for linear elements and piecewise planar interfaces. Higher-order convergence for arbitrary curved interfaces relies on two major issues: (i) an accurate quadrature of the Galerkin weak form for the cut elements and (ii) a careful formulation of the enrichment, which should preclude any problems in the blending elements. For (i), we employ a strategy of subdividing the elements into subcells with only one curved side. Reference elements that are higher-order on only one side are then used to map the integration points to the real element. For (ii), we find that enrichments for strong discontinuities are easily extended to higher-order accuracy. In contrast, problems in blending elements may hinder optimal convergence for weak discontinuities. Different formulations are investigated, including the corrected XFEM. Numerical results for several test cases involving strong or weak curved discontinuities are presented. Quadratic and cubic approximations are investigated. Optimal convergence rates are achieved using the standard XFEM for the case of a strong discontinuity. Close-to-optimal convergence rates for the case of a weak discontinuity are achieved using the corrected XFEM. Copyright © 2009 John Wiley & Sons, Ltd. [source] A modified node-to-segment algorithm passing the contact patch testINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009Giorgio Zavarise Abstract Several investigations have shown that the classical one-pass node-to-segment (NTS) algorithms for the enforcement of contact constraints fail the contact patch test. This implies that the algorithms may introduce solution errors at the contacting surfaces, and these errors do not necessarily decrease with mesh refinement. The previous research has mainly focused on the Lagrange multiplier method to exactly enforce the contact geometry conditions. The situation is even worse with the penalty method, due to its inherent approximation that yields a solution affected by a non-zero penetration. The aim of this study is to analyze and improve the contact patch test behavior of the one-pass NTS algorithm used in conjunction with the penalty method for 2D frictionless contact. The paper deals with the case of linear elements. For this purpose, several sequential modifications of the basic formulation have been considered, which yield incremental improvements in results of the contact patch test. The final proposed formulation is a modified one-pass NTS algorithm which is able to pass the contact patch test also if used in conjunction with the penalty method. In other words, this algorithm is able to correctly reproduce the transfer of a constant contact pressure with a constant proportional penetration. Copyright © 2009 John Wiley & Sons, Ltd. [source] Practical evaluation of five partly discontinuous finite element pairs for the non-conservative shallow water equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2010Richard Comblen Abstract This paper provides a comparison of five finite element pairs for the shallow water equations. We consider continuous, discontinuous and partially discontinuous finite element formulations that are supposed to provide second-order spatial accuracy. All of them rely on the same weak formulation, using Riemann solver to evaluate interface integrals. We define several asymptotic limit cases of the shallow water equations within their space of parameters. The idea is to develop a comparison of these numerical schemes in several relevant regimes of the subcritical shallow water flow. Finally, a new pair, using non-conforming linear elements for both velocities and elevation (P,P), is presented, giving optimal rates of convergence in all test cases. P,P1 and P,P1 mixed formulations lack convergence for inviscid flows. P,P2 pair is more expensive but provides accurate results for all benchmarks. P,P provides an efficient option, except for inviscid Coriolis-dominated flows, where a small lack of convergence is observed. Copyright © 2009 John Wiley & Sons, Ltd. [source] An approximate projection method for incompressible flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2002David E. Stevens This paper presents an approximate projection method for incompressible flows. This method is derived from Galerkin orthogonality conditions using equal-order piecewise linear elements for both velocity and pressure, hereafter Q1Q1. By combining an approximate projection for the velocities with a variational discretization of the continuum pressure Poisson equation, one eliminates the need to filter either the velocity or pressure fields as is often needed with equal-order element formulations. This variational approach extends to multiple types of elements; examples and results for triangular and quadrilateral elements are provided. This method is related to the method of Almgren et al. (SIAM J. Sci. Comput. 2000; 22: 1139,1159) and the PISO method of Issa (J. Comput. Phys. 1985; 62: 40,65). These methods use a combination of two elliptic solves, one to reduce the divergence of the velocities and another to approximate the pressure Poisson equation. Both Q1Q1 and the method of Almgren et al. solve the second Poisson equation with a weak error tolerance to achieve more computational efficiency. A Fourier analysis of Q1Q1 shows that a consistent mass matrix has a positive effect on both accuracy and mass conservation. A numerical comparison with the widely used Q1Q0 (piecewise linear velocities, piecewise constant pressures) on a periodic test case with an analytic solution verifies this analysis. Q1Q1 is shown to have comparable accuracy as Q1Q0 and good agreement with experiment for flow over an isolated cubic obstacle and dispersion of a point source in its wake. Copyright © 2002 John Wiley & Sons, Ltd. [source] A fractional adaptation law for sliding mode controlINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 10 2008Mehmet Önder Efe Abstract This paper presents a novel parameter tuning law that forces the emergence of a sliding motion in the behavior of a multi-input multi-output nonlinear dynamic system. Adaptive linear elements are used as controllers. Standard approach to parameter adjustment employs integer order derivative or integration operators. In this paper, the use of fractional differentiation or integration operators for the performance improvement of adaptive sliding mode control systems is presented. Hitting in finite time is proved and the associated conditions with numerical justifications are given. The proposed technique has been assessed through a set of simulations considering the dynamic model of a two degrees of freedom direct drive robot. It is seen that the control system with the proposed adaptation scheme provides (i) better tracking performance, (ii) suppression of undesired drifts in parameter evolution, (iii) a very high degree of robustness and improved insensitivity to disturbances and (iv) removal of the controller initialization problem. Copyright © 2008 John Wiley & Sons, Ltd. [source] A quasi-planar incident wave excitation for time-domain scattering analysis of periodic structuresINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 5 2006David Degerfeldt Abstract We present a quasi-planar incident wave excitation for time-domain scattering analysis of periodic structures. It uses a particular superposition of plane waves that yields an incident wave with the same periodicity as the periodic structure itself. The duration of the incident wave is controlled by means of its frequency spectrum or, equivalently, the angular spread in its constituting plane waves. Accuracy and convergence properties of the method are demonstrated by scattering computations for a planar dielectric half-space. Equipped with the proposed source, a time-domain solver based on linear elements yields an error of roughly 1% for a resolution of 20 points per wavelength and second-order convergence is achieved for smooth scatterers. Computations of the scattering characteristics for a sinusoidal surface and a random rough surface show similar performance. Copyright © 2006 John Wiley & Sons, Ltd. [source] Plant functional group composition and large-scale species richness in European agricultural landscapesJOURNAL OF VEGETATION SCIENCE, Issue 1 2008Jaan Liira Abstract Question: Which are the plant functional groups responding most clearly to agricultural disturbances? Which are the relative roles of habitat availability, landscape configuration and agricultural land use intensity in affecting the functional composition and diversity of vascular plants in agricultural landscapes? Location: 25 agricultural landscape areas in seven European countries. Methods: We examined the plant species richness and abundance in 4 km × 4 km landscape study sites. The plant functional group classification was derived from the BIOLFLOR database. Factorial decomposition of functional groups was applied. Results: Natural habitat availability and low land use intensity supported the abundance and richness of perennials, sedges, pteridophytes and high nature quality indicator species. The abundance of clonal species, C and S strategists was also correlated with habitat area. An increasing density of field edges explained a decrease in richness of high nature quality species and an increase in richness of annual graminoids. Intensive agriculture enhanced the richness of annuals and low nature quality species. Conclusions: Habitat patch availability and habitat quality are the main drivers of functional group composition and plant species richness in European agricultural landscapes. Linear elements do not compensate for the loss of habitats, as they mostly support disturbance tolerant generalist species. In order to conserve vascular plant species diversity in agricultural landscapes, the protection and enlargement of existing patches of (semi-) natural habitats appears to be more effective than relying on the rescue effect of linear elements. This should be done in combination with appropriate agricultural management techniques to limit the effect of agrochemicals to the fields. [source] Modelling of non linear elements using an extended iterative methodMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 1 2007Mohamed Glaoui Abstract This paper presents an iterative method based on the wave concept for investigation of structures including Non-linear components. The principle of the iterative method consists to establishing a relationship between incident and reflected waves in order to characterize the studied structure. A passage from frequency domain to time domain is used to describe the behavior of a non-linear transmission line (NLTL) including eight Varactor diodes. It is demonstrated that the NLTL plays the role of a delay time line (DTL). The reflected and transmission coefficients are determined. The numerical results are compared with published data. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 143,147, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22079 [source] Finite element approximation of a forward and backward anisotropic diffusion model in image denoising and form generalizationNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2008Carsten Ebmeyer Abstract A new forward,backward anisotropic diffusion model is introduced. The two limit cases are the Perona-Malik equation and the Total Variation flow model. A fully discrete finite element scheme is studied using C0 -piecewise linear elements in space and the backward Euler difference scheme in time. A priori estimates are proven. Numerical results in image denoising and form generalization are presented.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 [source] On the subdomain-Galerkin/least squares method for 2- and 3-D mixed elliptic problems with reaction termsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2002Suh-Yuh Yang Abstract In this article we apply the subdomain-Galerkin/least squares method, which is first proposed by Chang and Gunzburger for first-order elliptic systems without reaction terms in the plane, to solve second-order non-selfadjoint elliptic problems in two- and three-dimensional bounded domains with triangular or tetrahedral regular triangulations. This method can be viewed as a combination of a direct cell vertex finite volume discretization step and an algebraic least-squares minimization step in which the pressure is approximated by piecewise linear elements and the flux by the lowest order Raviart-Thomas space. This combined approach has the advantages of both finite volume and least-squares methods. Among other things, the combined method is not subject to the Ladyzhenskaya-Babus,ka-Brezzi condition, and the resulting linear system is symmetric and positive definite. An optimal error estimate in the H1(,) × H(div; ,) norm is derived. An equivalent residual-type a posteriori error estimator is also given. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 738,751, 2002; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/num.10030. [source] Nonconforming Galerkin methods for the Helmholtz equationNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2001Jim Douglas Jr. Abstract Nonconforming Galerkin methods for a Helmholtz-like problem arising in seismology are discussed both for standard simplicial linear elements and for several new rectangular elements related to bilinear or trilinear elements. Optimal order error estimates in a broken energy norm are derived for all elements and in L2 for some of the elements when proper quadrature rules are applied to the absorbing boundary condition. Domain decomposition iterative procedures are introduced for the nonconforming methods, and their convergence at a predictable rate is established. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 475,494, 2001 [source] | ||||||||||||||||||||||