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- Title
A Stable Mixed Element Method for the Biharmonic Equation with First-Order Function Spaces.
- Authors
Zheng Li; Shuo Zhang
- Abstract
This paper studies the mixed element method for the boundary value problem of the biharmonic equation ▵2u = f in two dimensions. We start from a u ∼ ▿ ∼ 2u ∼ div 2u formulation that is discussed in [4] and construct its stability on H10(Ω) × H10(Ω) × L2sym(Ω) × H-1(div). Then we utilise the Helmholtz decomposition of H-1(div,Ω) and construct a new formulation stable on first-order and zero-order Sobolev spaces. Finite element discretisations are then given with respect to the new formulation, and both theoretical analysis and numerical verification are given.
- Subjects
NUMERICAL solutions to boundary value problems; NUMERICAL solutions to biharmonic equations; FUNCTION spaces
- Publication
Computational Methods in Applied Mathematics, 2017, Vol 17, Issue 4, p601
- ISSN
1609-4840
- Publication type
Article
- DOI
10.1515/cmam-2017-0002