1.1. Mesh data structure. The matrices node(1:N,1:d) and elem(1:NT,1:d+1) are used to represent a d-dimensional triangulation embedded in R, where N is the number of vertices and NT is the number of elements. These two matrices represent two different structure of a triangulation: elem for the topology and node for the geometric embedding. The matrix elem represents a set of abstract simplices....

Abstract. This work establishes a formal derivation of local projection stabilized methods as a result of an enriched Petrov-Galerkin strategy for the Stokes problem. Both velocity and pressure finite element spaces are enhanced with solutions of residual-based local problems, and then the static condensation procedure is applied to derive new methods. The approach keeps degrees of freedom unch...

Cover picture: a typical part of the Dutch dike, divided in sections and modeled by finite elements. LEGAL NOTICE The publisher is not responsible for the use which might be made of following information. PRINTED IN THE NETHERLANDS In the name of who creates and owns souls and thoughts, the most precious things that one can think about. A. Ferdousi, 970 AC This book is dedicated to Ali and Ghad...

We consider precondition of linear systems resulting from the finite volume element method (FVEM) for elliptic boundary value problems. With the help of the interpolation operator from a trial space to a test space and the operator induced by the FVEM bilinear form, we show that both wavelet preconditioners and multilevel preconditioners designed originally for the finite element method for the...

In this article, we propose and analyze an effective Hessian recovery strategy for the Lagrangian finite element method of arbitrary order. We prove that the proposed Hessian recovery method preserves polynomials of degree k + 1 on general unstructured meshes and superconverges at a rate of O(hk) on mildly structured meshes. In addition, the method is proved to be ultraconvergent (two orders hi...

The paper focuses on the numerical treatment of transient acoustic problems using finite element (FE) and boundary element (BE) methods. The FE method relies on a pressure formulation and the use of an implicit integration schemes for solving the related second-order differential system. The procedure is shown on cavity (interior) problems but can be extended to exterior problems using the DtN ...

finite element and boundary methods in structural finite element and boundary methods in structural finite element and boundary methods in structural finite element and boundary methods in structural finite element and boundary methods in structural finite element and boundary methods in structural finite element and boundary methods in structural introduction to finite element vibration analys...

We continue our work on adaptive nite element methods with a study of time discretization of analytic semigroups. We prove optimal a priori and a posteriori error estimates for the discontinuous Galerkin method showing, in particular, that analytic semigroups allow long-time integration without error accumulation. 1. Introduction This paper is a continuation of the series of papers 1], 2], 3], ...

Abstract Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge ...