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The influence of boundary approximation on transfer operators between non‐nested meshes
Author(s) -
Dickopf Thomas,
Krause Rolf
Publication year - 2013
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201310261
Subject(s) - polygon mesh , finite element method , matching (statistics) , mathematics , boundary (topology) , projection (relational algebra) , volume mesh , flexibility (engineering) , computer science , mesh generation , geometry , algorithm , mathematical analysis , structural engineering , engineering , statistics
Abstract Finite element methods with non‐matching meshes can offer increased flexibility in many applications. Although the specific reasons for the use of non‐matching meshes are apparently diverse, the common difficulty in all these numerical methods is the transfer of finite element approximation associated with one mesh to finite element approximation associated with another mesh. This paper complements previous quantitative studies of transfer operators between finite element spaces associated with unrelated meshes (T. Dickopf, R. Krause, Evaluating local approximations of the L 2 ‐orthogonal projection between non‐nested finite element spaces, Tech. Rep. 2012‐01, Institute of Computational Science, Università della Svizzera italiana, 2012). We study the important use case in which functions are mapped between a regular background mesh and an unstructured mesh of a complex geometry. Here, the former does not approximate the latter. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)