Anisotropic hp-mesh optimization technique based on the continuous mesh and error models. (1st July 2017)

• Record Type: Journal Article
• Authors: Dolejší, Vít; May, Georg; Roskovec, Filip; Solin, Pavel
• Is Part Of: Computers & mathematics with applications. Volume 74:issue 1(2017)
• Page Start: 45
• Page End: 63
• Publication Date: 2017-07-01
• Subjects: hp-methods -- Anisotropic mesh adaptation -- Continuous mesh model -- Continuous error model -- Mesh optimization; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.12.015
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We develop a new mesh adaptive technique for the numerical solution of partial differential equations (PDEs) using the h p -version of the finite element method ( h p -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 h p -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 h p -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 h p -mesh in the sense of the mesh optimization problem. Several numerical examples demonstrating the efficiency and applicability of the new method are presented.