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Bernstein Polynomials (bernstein + polynomial)
Selected AbstractsBernstein Ritz-Galerkin method for solving an initial-boundary value problem that combines Neumann and integral condition for the wave equationNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2010S.A. Yousefi Abstract In this article, the Ritz-Galerkin method in Bernstein polynomial basis is implemented to give an approximate solution of a hyperbolic partial differential equation with an integral condition. We will deal here with a type of nonlocal boundary value problem, that is, the solution of a hyperbolic partial differential equation with a nonlocal boundary specification. The nonlocal conditions arise mainly when the data on the boundary cannot be measured directly. The properties of Bernstein polynomial and Ritz-Galerkin method are first presented, then Ritz-Galerkin method is used to reduce the given hyperbolic partial differential equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique presented in this article. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 [source] On the C1 continuous discretization of non-linear gradient elasticity: A comparison of NEM and FEM based on Bernstein,Bézier patchesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010P. Fischer Abstract In gradient elasticity, the appearance of strain gradients in the free energy density leads to the need of C1 continuous discretization methods. In the present work, the performances of C1 finite elements and the C1 Natural Element Method (NEM) are compared. The triangular Argyris and Hsieh,Clough,Tocher finite elements are reparametrized in terms of the Bernstein polynomials. The quadrilateral Bogner,Fox,Schmidt element is used in an isoparametric framework, for which a preprocessing algorithm is presented. Additionally, the C1 -NEM is applied to non-linear gradient elasticity. Several numerical examples are analyzed to compare the convergence behavior of the different methods. It will be illustrated that the isoparametric elements and the NEM show a significantly better performance than the triangular elements. Copyright © 2009 John Wiley & Sons, Ltd. [source] c-Type method of unified CAMG and FEA.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 20032D non-linear, 3D linear, Part 1: Beam, arch mega-elements Abstract Computer-aided mesh generation (CAMG) dictated solely by the minimal key set of requirements of geometry, material, loading and support condition can produce ,mega-sized', arbitrary-shaped distorted elements. However, this may result in substantial cost saving and reduced bookkeeping for the subsequent finite element analysis (FEA) and reduced engineering manpower requirement for final quality assurance. A method, denoted as c-type, has been proposed by constructively defining a finite element space whereby the above hurdles may be overcome with a minimal number of hyper-sized elements. Bezier (and de Boor) control vectors are used as the generalized displacements and the Bernstein polynomials (and B-splines) as the elemental basis functions. A concomitant idea of coerced parametry and inter-element continuity on demand unifies modelling and finite element method. The c-type method may introduce additional control, namely, an inter-element continuity condition to the existing h-type and p-type methods. Adaptation of the c-type method to existing commercial and general-purpose computer programs based on a conventional displacement-based finite element method is straightforward. The c-type method with associated subdivision technique can be easily made into a hierarchic adaptive computer method with a suitable a posteriori error analysis. In this context, a summary of a geometrically exact non-linear formulation for the two-dimensional curved beams/arches is presented. Several beam problems ranging from truly three-dimensional tortuous linear curved beams to geometrically extremely non-linear two-dimensional arches are solved to establish numerical efficiency of the method. Incremental Lagrangian curvilinear formulation may be extended to overcome rotational singularity in 3D geometric non-linearity and to treat general material non-linearity. Copyright © 2003 John Wiley & Sons, Ltd. [source] On the image of the limit q -Bernstein operatorMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 15 2009Sofiya Ostrovska Abstract The limit q -Bernstein operator Bq emerges naturally as an analogue to the Szász,Mirakyan operator related to the Euler distribution. Alternatively, Bq comes out as a limit for a sequence of q -Bernstein polynomials in the case 0
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