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A finite element method on composite grids based on Nitsche’s method. (English) Zbl 1031.65128
The authors introduce a finite element method on overlapping grids on domains in 2 or 3 dimensions. The implementation permits a great deal of freedom in the geometry of the grids, because one-sided approximations of derivatives are used at the interface. Smoothness of the solution across the grid interface is attained by a penalty method, generalizing work of J. Nitsche [Abh. Math. Semin. Univ. Hamb. 36, 9-15 (1971; Zbl 0229.65079)]. The method is applied to the Poisson equation.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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References:
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