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A posteriori error control for the finite cell method
Author(s) -
Di Stolfo Paolo,
Düster Alexander,
Kollmannsberger Stefan,
Rank Ernst,
Schröder Andreas
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900419
Subject(s) - discretization error , a priori and a posteriori , discretization , quadrature (astronomy) , finite element method , computer science , residual , error detection and correction , error analysis , adaptive quadrature , method of mean weighted residuals , mathematics , mathematical optimization , algorithm , control theory (sociology) , control (management) , artificial intelligence , mathematical analysis , engineering , electronic engineering , philosophy , structural engineering , epistemology , galerkin method
The paper presents some concepts of the finite cell method and discusses a posteriori error control for this approach. The focus is on the application of the dual weighted residual approach (DWR), which enables the control of the error with respect to a user‐defined quantity of interest. Since both the discretization error and the quadrature error are estimated, the application of the DWR approach provides an adaptive strategy which equilibrates the error contributions resulting from discretization and quadrature. The strategy consists in refining either the finite cell mesh or its associated quadrature mesh. Numerical experiments confirm the performance of the error control and the adaptive scheme for a non‐linear problem in 2D.