PDE-independent adaptive hp-FEM based on hierarchic extension of finite element spaces

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:233

Article; Proceedings Paper

Solin, Pavel^1,2  Andrs, David^1,2  Cerveny, Jakub² 

[1] Univ Nevada, Dept Math & Stat, Reno, NV 89557 USA

[2] Inst Thermomech, Prague, Czech Republic

关键词: Automatic adaptivity;    Higher-order finite elements;    hp-FEM;    Hierarchic basis extension;    Embedded stiffness matrices;   

DOI  :  10.1016/j.cam.2009.05.030

来源: Elsevier

【 摘 要 】

We present a novel approach to automatic adaptivity in higher-order finite element methods (hp-FEM) which is free of analytical error estimates. This means that a computer code based on this approach can be used to solve adaptively a wide range of PDE problems. A posteriori error estimation is done computationally via hierarchic extension of finite element spaces. This is an analogy to embedded higher-order methods for ODE. The adaptivity process yields a sequence of embedded stiffness matrices which are solved efficiently using a simple combined direct-iterative algorithm. The methodology works equally well for standard low-order FEM and for the hp-FEM. Numerical examples are presented. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free