A comparison of simplicial and block finite elements

0351143 - MÚ 2011 RIV DE eng C - Conference Paper (international conference)
Korotov, S. - Vejchodský, Tomáš
A comparison of simplicial and block finite elements.
Numerical Mathematics and Advanced Applications 2009. Berlin: Springer, 2010 - (Kreiss, G.; Lötstedt, P.; Malqvist, A.), s. 533-541. ISBN 978-3-642-11794-7.
[ENUMATH 2009 /8./. Uppsala (SE), 29.06.2009-03.07.2009]
R&D Projects: GA AV ČR IAA100760702; GA ČR(CZ) GA102/07/0496
Institutional research plan: CEZ:AV0Z10190503
Keywords : finite element method * simples * blocks * discrete maximum principle * mesh refinement
Subject RIV: BA - General Mathematics
http://link.springer.com/chapter/10.1007%2F978-3-642-11795-4_57

In this note we discuss and compare the performance of the finite element method (FEM) on two popular types of meshes - simplicial and block ones. A special emphasis is put on the validity of discrete maximum principles and on associated (geometric) mesh generation/refinement issues in higher dimensions. As a result, we would recommend to carefully reconsider the common belief that the simplicial finite elements are very convenient to describe complicated geometries (which appear in real-life problems), and also that the block finite elements, due to their simplicity, should be used if the geometry of the solution domain allows that.
Permanent Link: http://hdl.handle.net/11104/0190955