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Finite element methods on non-conforming grids by penalizing the matching constraint. (English) Zbl 1043.65124

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 \(h^{1-\delta}\), \(0 < \delta \leq 1/2\).
A suboptimal error estimate of order \(h| \log h| \) for this method was proven by R. D. Lazarov, J. E. Pasciak, J. Schöberl and 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)].

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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References:

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