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Discrete Problem (discrete + problem)
Selected AbstractsPiecewise divergence-free discontinuous Galerkin methods for Stokes flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2008Peter Hansbo Abstract In this paper, we consider different possibilities of using divergence-free discontinuous Galerkin methods for the Stokes problem in order to eliminate the pressure from the discrete problem. We focus on three different approaches: one based on a C0 approximation of the stream function in two dimensions (the vector potential in three dimensions), one based on the non-conforming Morley element (which corresponds to a divergence-free non-conforming Crouzeix,Raviart approximation of the velocities), and one fully discontinuous Galerkin method with a stabilization of the pressure that allows the edgewise elimination of the pressure variable before solving the discrete system. We limit the analysis in the stream function case to two spatial dimensions, while the analysis of the fully discontinuous approach is valid also in three dimensions. Copyright © 2006 John Wiley & Sons, Ltd. [source] Heat conduction and radiative heat exchange in cellular structures using flat shell elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2006J. B. Colliat Abstract We developed in this paper a variational formulation of heat diffusion equation applicable to the flat shell context and cellular structures. For this purpose, we introduce the average mid-surface temperature field, through-the-thickness gradient and their dual generalized fluxes. Moreover, we introduced radiative heat exchange in the same way, which leads to a non-linear and unsymmetrical thermal discrete problem. The model performance is illustrated by several numerical examples concerning cellular structures like hollow clay bricks submitted to thermal loading. Thermo-mechanical coupling for such structure which is well adapted to the shell-like modelling approach, is presented in the elastic regime with the numerical results concerning temperature field and forces. Copyright © 2005 John Wiley & Sons, Ltd. [source] On the application of slip boundary condition on curved boundariesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2004Marek Behr Abstract Hydrodynamic simulations of sloshing phenomena often involve the application of slip boundary condition at the wetted surfaces. If these surfaces are curved, the ambiguous nature of the normal vector in the discretized problem can interfere with the application of such a boundary condition. Even the use of consistent normal vectors, preferred from the point of view of conservation, does not assure good approximation of the continuum slip condition in the discrete problem, and non-physical recirculating flow fields may be observed. As a remedy, we consider the Navier slip condition, and more successfully, the so-called BC-free boundary condition. Copyright © 2004 John Wiley & Sons, Ltd. [source] A time-marching finite element method for an electromagnetic scattering problemMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 12 2003Tri Van Abstract In this paper, Newmark time-stepping scheme and edge elements are used to numerically solve the time-dependent scattering problem in a three-dimensional polyhedral cavity. Finite element methods based on the variational formulation derived in Van and Wood (Adv. Comput. Math., to appear) are considered. Existence and uniqueness of the discrete problem is proved by using Babuska,Brezzi theory. Finite element error estimate and stability of the Newmark scheme are also established. Copyright © 2003 John Wiley & Sons, Ltd. [source] Multigrid methods for the symmetric interior penalty method on graded meshesNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 6 2009S. C. Brenner Abstract The symmetric interior penalty (SIP) method on graded meshes and its fast solution by multigrid methods are studied in this paper. We obtain quasi-optimal error estimates in both the energy norm and the L2 norm for the SIP method, and prove uniform convergence of the W -cycle multigrid algorithm for the resulting discrete problem. The performance of these methods is illustrated by numerical results. Copyright © 2009 John Wiley & Sons, Ltd. [source] Characteristic-mixed covolume methods for advection-dominated diffusion problemsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 9 2006Zhangxin Chen Abstract Characteristic-mixed covolume methods for time-dependent advection-dominated diffusion problems are developed and studied. The diffusion term in these problems is discretized using covolume methods applied to the mixed formulation of the problems on quadrilaterals, and the temporal differentiation and advection terms are treated by characteristic tracking schemes. Three characteristic tracking schemes are studied in the context of mixed covolume methods: the modified method of characteristics, the modified method of characteristics with adjusted advection, and the Eulerian,Lagrangian localized adjoint method. The proposed methods preserve the conceptual and computational merits of both characteristics-based schemes and the mixed covolume methods. Existence and uniqueness of a solution to the discrete problem arising from the methods is shown. Stability and convergence properties of these methods are also obtained; unconditionally stable results and error estimates of optimal order are established. Copyright © 2006 John Wiley & Sons, Ltd. [source] An adaptive multigrid iterative approach for frictional contact problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2006S. A. Mohamed Abstract The objective of this paper is the construction of a robust strategy towards adaptively solving Signorini's frictional contact problems. The frictional contact problem between a linearly elastic body and rigid foundation is formulated as a classical boundary value problem of the elastic body but associated with special inequality conditions on the contact surface. A new iterative approach is presented to solve the problem on a given mesh. In the first iteration the candidate nodes are assumed to be in micro-slip contact and then proceeding to update the contact status according to the actual displacements and stresses obtained at the end of each increment. An efficient multigrid method is developed to solve the discrete problems of different iterations. The proposed iterative procedure is integrated with an error indicator and automatic grid generator to construct an adaptive multigrid method. Numerical results of the convergence rates, automatically generated grid sequence, contact stresses and strains as well as two parametric studies are presented to prove the efficiency of the proposal. Copyright © 2005 John Wiley & Sons, Ltd. [source] A new consistent discrete-velocity model for the Boltzmann equationMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2002Vladislav A. Panferov This paper discusses the convergence of a new discrete-velocity model to the Boltzmann equation. First the consistency of the collision integral approximation is proved. Based on this we prove the convergence of solutions for a modified model to renormalized solutions of the Boltzmann equation. In a numerical example, the solutions to the discrete problems are compared with the exact solution of the Boltzmann equation in the space-homogeneous case. Copyright © 2002 John Wiley & Sons, Ltd. [source] A multilevel method for discontinuous Galerkin approximation of three-dimensional anisotropic elliptic problemsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 5 2008J. K. Kraus Abstract We construct optimal order multilevel preconditioners for interior-penalty discontinuous Galerkin (DG) finite element discretizations of three-dimensional (3D) anisotropic elliptic boundary-value problems. In this paper, we extend the analysis of our approach, introduced earlier for 2D problems (SIAM J. Sci. Comput., accepted), to cover 3D problems. A specific assembling process is proposed, which allows us to characterize the hierarchical splitting locally. This is also the key for a local analysis of the angle between the resulting subspaces. Applying the corresponding two-level basis transformation recursively, a sequence of algebraic problems is generated. These discrete problems can be associated with coarse versions of DG approximations (of the solution to the original variational problem) on a hierarchy of geometrically nested meshes. A new bound for the constant , in the strengthened Cauchy,Bunyakowski,Schwarz inequality is derived. The presented numerical results support the theoretical analysis and demonstrate the potential of this approach. Copyright © 2007 John Wiley & Sons, Ltd. [source] On Small-Sample Confidence Intervals for Parameters in Discrete DistributionsBIOMETRICS, Issue 3 2001Alan Agresti Summary. The traditional definition of a confidence interval requires the coverage probability at any value of the parameter to be at least the nominal confidence level. In constructing such intervals for parameters in discrete distributions, less conservative behavior results from inverting a single two-sided test than inverting two separate one-sided tests of half the nominal level each. We illustrate for a variety of discrete problems, including interval estimation of a binomial parameter, the difference and the ratio of two binomial parameters for independent samples, and the odds ratio. [source] | |||||||||||||