Asymptotic exactness of some Bank--Weiser error estimator for quadratic triangular finite element
Bull. Korean Math. Soc. 2020 Vol. 57, No. 2, 393-406
Published online March 31, 2020
Kwang-Yeon Kim, Ju-Seong Park
Kangwon National University; Kangwon National University
Abstract : We analyze a posteriori error estimator for the conforming $P2$ finite element on triangular meshes which is based on the solution of local Neumann problems. This error estimator extends the one for the conforming $P1$ finite element proposed in \cite{Bank-Weiser85}. We prove that it is asymptotically exact for the Poisson equation when the underlying triangulations are mildly structured and the solution is smooth enough.
Keywords : A posteriori error estimator, asymptotic exactness, quadratic finite element method
MSC numbers : Primary 65N30, 65N15
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