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Title: Space-time adaptive $hp$-FEM: Methodology overview (English)
Author: Šolín, Pavel
Author: Segeth, Karel
Author: Doležel, Ivo
Language: English
Journal: Programs and Algorithms of Numerical Mathematics
Volume: Proceedings of Seminar. Dolní Maxov, June 1-6, 2008
Issue: 2008
Pages: 185-200
Category: math
Summary: We present a new class of self-adaptive higher-order finite element methods ($hp$-FEM) which are free of analytical error estimates and thus work equally well for virtually all PDE problems ranging from simple linear elliptic equations to complex time-dependent nonlinear multiphysics coupled problems. The methods do not contain any tuning parameters and work reliably with both low- and high-order finite elements. The methodology was used to solve various types of problems including thermoelasticity, microwave heating, flow of thermally conductive liquids etc. In this paper we use a combustion problem described by a system of two coupled nonlinear parabolic equations for illustration. The algorithms presented in this paper are available under the GPL license in the form of a modular C++ library HERMES. ()
MSC: 65M60
idZBL: Zbl 05802259
Date available: 2015-09-08T11:37:26Z
Last updated: 2015-12-04
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