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Non-conforming spectral method for second order elliptic problems in 3D. (English) Zbl 0835.65129
Summary: This paper deals with the extension of the non-conforming mortar spectral element method to the 3D case. We first propose a 2D version of the original method which consists in relaxing the matching constraints at the vertices. This version provides optimal error estimates and turns out to be more suitable for parallel implementation. Then, we generalize it to 3D elliptic problems and prove optimal a priori error estimates for many generic situations including those encountered in sliding meshes decompositions. We obtain quasi-optimal approximations for arbitrary decompositions.

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65Y05 Parallel numerical computation
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation