Space-time adaptive $hp$-FEM: Methodology overview

Šolín, Pavel, Segeth, Karel, and Doležel, Ivo. "Space-time adaptive $hp$-FEM: Methodology overview." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics AS CR, 2008. 185-200. <http://eudml.org/doc/271346>.

@inProceedings{Šolín2008,
abstract = {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.},
author = {Šolín, Pavel, Segeth, Karel, Doležel, Ivo},
booktitle = {Programs and Algorithms of Numerical Mathematics},
location = {Prague},
pages = {185-200},
publisher = {Institute of Mathematics AS CR},
title = {Space-time adaptive $hp$-FEM: Methodology overview},
url = {http://eudml.org/doc/271346},
year = {2008},
}

TY - CLSWK
AU - Šolín, Pavel
AU - Segeth, Karel
AU - Doležel, Ivo
TI - Space-time adaptive $hp$-FEM: Methodology overview
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2008
CY - Prague
PB - Institute of Mathematics AS CR
SP - 185
EP - 200
AB - 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.
UR - http://eudml.org/doc/271346
ER -