Release Time:2021-09-29  Hits:

Indexed by: Journal Article

Date of Publication: 2021-01-10

Journal: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

Volume: 36

Issue: 6

Page Number: 2018-2034

ISSN: 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.