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Zbl 1043.65124
Boillat, Eric
Finite element methods on non-conforming grids by penalizing the matching constraint. (English)
[J] M2AN, Math. Model. Numer. Anal. 37, No. 2, 357-372 (2003). ISSN 0764-583X; ISSN 1290-3841/e

The paper deals with the finite element approximation of second order selfadjoint elliptic problems on non-matching grids. The jump along the interface, where the meshes do not match, is penalized by a wieght of $h^{-1}$, with $h$ the mesh size. In contrast to the popular mortar technique this leads to a symmetric and positive definite discrete problem. The authors prove a non optimal error estimate of order $h^{1-\delta}$, $0 < \delta \leq 1/2$. \par A suboptimal error estimate of order $h\vert \log h\vert $ for this method was proven by {\it R. D. Lazarov}, {\it J. E. Pasciak}, {\it J. Schöberl} and {\it P. S. Vassilevski} [Almost optimal interior penalty discontinuous approximations of symmetric elliptic problems on non-matching grids, Numer. Math. 96, No. 2, 295--315 (2003)].
[Raico R. D. Lazarov (College Station)]

MSC 2000:: *65N30 Finite numerical methods (BVP of PDE)
65F10 Iterative methods for linear systems
65N12 Stability and convergence of numerical methods (BVP of PDE)
35J25 Second order elliptic equations, boundary value problems
65N50 Mesh generation and refinement (BVP of PDE)

Keywords: elliptic problems; error estimate; finite element methods; non-matching grids; penalty technique

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