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A locally modified parametric finite element method for interface problems. (English) Zbl 1310.65145
The authors are concerned with a finite element technique able to solve accurately a 2D interface problem attached to a second-order elliptic boundary value problem. The interface splits the domain in two non-overlapping subdomains. On this interface the solution is assumed to be continuous. However, its normal derivative oriented to the interior of the domain, may have a jump. The authors introduce a technique which combine a fitted approach, based on a mixed triangular-quadrilateral mesh, with an implicit parametric locally adapted finite element basis. The technique assumes neither an enrichment of the bases nor a modification of the mesh, and the condition number of the system matrix remains bounded. Some hints on the efficient implementation of the practical codes are provided and some numerical experiments are carried out in order to underline the capabilities of the proposed technique.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds 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
65F35 Numerical computation of matrix norms, conditioning, scaling
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