A Comparison of Simplicial and Block Finite Elements

Sergey Korotov () and Tomáš Vejchodský ()
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Sergey Korotov: Tampere University of Technology, Institute of Mathematics
Tomáš Vejchodský: Academy of Sciences, Institute of Mathematics

A chapter in Numerical Mathematics and Advanced Applications 2009, 2010, pp 533-541 from Springer

Abstract: Abstract 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.

Keywords: Stiffness Matrix; Homogeneous Dirichlet Boundary Condition; Hanging Node; Simplicial Mesh; Discrete Maximum Principle (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-3-642-11795-4_57

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