Anisotropic hp-mesh optimization technique based on the continuous mesh and error models

• ID: 2750, RIV: 10361204
• ISSN: 0898-1221, ISBN: not specified
• source: Computers and Mathematics with Applications
• keywords: hp-methods; Anisotropic mesh adaptation; Continuous mesh model; Continuous error model; Mesh optimization
• authors: Vít Dolejší, Georg May, Filip Roskovec, Pavel Solin
• authors from KNM: Dolejší Vít, Roskovec Filip

Abstract

We develop a new mesh adaptive technique for the numerical solution of partial differential equations (PDEs) using the hp-version of the finite element method (hp-FEM). The technique uses a combination of approximation and interpolation error estimates to generate anisotropic triangular elements as well as appropriate polynomial approximation degrees. We present a hp-version of the continuous mesh model as well as the continuous error model which are used for the formulation of a mesh optimization problem. Solving the optimization problem leads to hp-mesh with the smallest number of degrees of freedom, under the constraint that the approximate solution has an error estimate below a given tolerance. Further, we propose an iterative algorithm to find a suitable anisotropic hp-mesh in the sense of the mesh optimization problem. Several numerical examples demonstrating the efficiency and applicability of the new method are presented.