PDE-independent adaptive -FEM based on hierarchic extension of finite element spaces
✍ Scribed by Pavel Solin; David Andrs; Jakub Cerveny; Miroslav Simko
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 762 KB
- Volume
- 233
- Category
- Article
- ISSN
- 0377-0427
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✦ Synopsis
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.