Startseite A Stable Mixed Element Method for the Biharmonic Equation with First-Order Function Spaces
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A Stable Mixed Element Method for the Biharmonic Equation with First-Order Function Spaces

  • Zheng Li und Shuo Zhang EMAIL logo
Veröffentlicht/Copyright: 13. April 2017

Abstract

This paper studies the mixed element method for the boundary value problem of the biharmonic equation Δ2u=f in two dimensions. We start from a uu2udiv2u formulation that is discussed in [4] and construct its stability on H01(Ω)×H~01(Ω)×L¯sym2(Ω)×H-1(div,Ω). 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.

MSC 2010: 35J35; 65N30

Award Identifier / Grant number: 91430215

Award Identifier / Grant number: 11101415

Award Identifier / Grant number: 11471026

Funding statement: The author Z. Li is thankful to the support from LSEC, AMSS during his visit and has been supported partially by NSFC grant no. 91430215. The author S. Zhang is partially supported by NSFC grant nos. 11101415 and 11471026.

Acknowledgements

The authors would like to thank the anonymous referees for their comments which helped us to improve the work.

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Received: 2016-11-11
Revised: 2017-2-22
Accepted: 2017-2-27
Published Online: 2017-4-13
Published in Print: 2017-10-1

© 2017 Walter de Gruyter GmbH, Berlin/Boston

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