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MESH PARTITIONING TECHNIQUES AND DOMAIN DECOMPOSITION METHODS
Edited by: F. Magoulès
On the Mortar Triangular Discrete Kirchoff Finite Elements for Elastic Plates
I3M, UMR CNRS 5149 Equipe ACSIOM, University of Montpellier II, France
C. Lacour, "On the Mortar Triangular Discrete Kirchoff Finite Elements for Elastic Plates", in F. Magoulès, (Editor), "Mesh Partitioning Techniques and Domain Decomposition Methods", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 13, pp 321-347, 2007. doi:10.4203/csets.17.13
Keywords: domain decomposition method, mortar method, discrete Kirchhoff triangles, consistency error, best fit error.
This chapter deals with the analysis of a non-conforming domain decomposition method, the mortar element method for solving systems of equations arising from Discrete Kirchhoff Triangles (DKT) finite element discretisation of a model fourth-order elliptic problem. We define the spaces of approximation and the decomposed discrete problem which of course relies on the variational formulation of the continuous one. We verify the uniform ellipticity and the uniform continuity (independent from the discretisation parameter) of the discrete bilinear form. We present a mathematical analysis of the method and derive optimal consistency error and best fit error.
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