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Robust residual‐ and recovery‐based a posteriori error estimators for a multipoint flux mixed finite element discretization of interface problems
Author(s) -
Du Shaohong,
Xie Xiaoping,
Cheng Pan
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22319
Subject(s) - estimator , finite element method , mathematics , discretization , a priori and a posteriori , residual , scalar (mathematics) , monotonic function , projection (relational algebra) , mixed finite element method , mathematical optimization , mathematical analysis , algorithm , geometry , statistics , philosophy , physics , epistemology , thermodynamics
We consider a posteriori error estimation for a multipoint flux mixed finite element method for two‐dimensional elliptic interface problems. Within the class of modified quasi‐monotonically distributed coefficients, we derive a residual‐type a posteriori error estimator of the weighted sum of the scalar and flux errors which is robust with respect to the jumps of the coefficients. Moreover, we develop robust implicit and explicit recovery‐type estimators through gradient recovery in an H (curl)‐conforming finite element space. In particular, we apply a modified L 2 projection in the implicit recovery procedure so as to reduce the computational cost of the recovered gradient. Numerical experiments confirm the theoretical results.