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Numerical quadratures and mortar methods. (English) Zbl 0911.65117
Bristeau, M.-O. (ed.) et al., Computational science for the 21st century. Dedicated to Prof. Roland Glowinski on the occasion of his 60th birthday. Symposium, Tours, France, May 5–7, 1997. Chichester: John Wiley & Sons. 119-128 (1997).
Our purpose, in this short contribution, is to focus on a practical problem of implementation. In the mortar method, the matching through the interfaces is done by equating moments and thus involves the computation of integrals. It is mandatory, expressely in the three-dimensional case, to use numerical quadratures to evaluate these integrals; if no attention is paid to compute them, the method can easily degenerate. One solution is to “pay the price” and have it done the most accurately possible based on the union of the meshes inherited from both sides (since this moment equation is on an interface that has one dimension less than the whole problem, it is thus still not too expensive), another possibility that is proposed here is to use consistant quadratures adapted only to one mesh.
For the entire collection see [Zbl 0889.00026].

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65D32 Numerical quadrature and cubature formulas
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation