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

Authors:
Pavel Solin;David Andrs;Jakub Cerveny;Miroslav Simko
Affiliations:
Department of Mathematics and Statistics, University of Nevada, Reno, USA and Institute of Thermomechanics, Dolejskova 5, Prague, Czech Republic;Department of Mathematics and Statistics, University of Nevada, Reno, USA and Institute of Thermomechanics, Dolejskova 5, Prague, Czech Republic;Institute of Thermomechanics, Dolejskova 5, Prague, Czech Republic;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

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.