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Composite Finite Elements for Elliptic Interface Problems
Author(s) -
Peterseim Daniel
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010323
Subject(s) - finite element method , discontinuity (linguistics) , discretization , interface (matter) , mathematics , boundary value problem , dirichlet distribution , mathematical analysis , classification of discontinuities , composite number , computer science , structural engineering , algorithm , engineering , bubble , maximum bubble pressure method , parallel computing
We present a Composite Finite Element Method for the approximation of linear elliptic boundary value problems of Dirichlet type with discontinuous coefficients. The challenge is the discontinuity of the coefficient (interface) which is not necessarily resolved by the underlying finite element mesh. The method is non‐conforming in the sense that shape functions preserve continuity across the interface only in an approximative way. However, the construction allows to balance the non‐conformity and the overall discretization error. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)