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Indexed by:期刊论文

Date of Publication:2021-01-10

Journal:NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

Volume:36

Issue:6

Page Number:2018-2034

ISSN No.:0749-159X

Key Words:biharmonic problem; high accuracy; nonconforming finite element

Abstract:This work gives the high accuracy analysis of a rectangular biharmonic element in arbitrarily high-dimensional cases. Given ann-rectangle, we construct the nonconforming finite element and show its explicit standard basis representation. We prove that, if then-rectangular mesh is uniform, this element can achieve a second order convergence rate in energy norm when applied to biharmonic problems. Numerical examples forn = 3 are also presented.