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**A finite element method for interface problems in domains with smooth boundaries and interfaces.**
*(English)*
Zbl 0868.65081

The authors give an analysis of a finite element method for nonhomogeneous second-order elliptic interface problems on smooth domains. It is shown that when the smooth domain is replaced by the polygonal domain and the boundary data are transferred in a natural way, the finite element method applied to the perturbed problem is optimal order accurate. Linear finite elements on quasiuniform triangulations are used. The considered approximation is shown to be robust in the regularity of the boundary data in the sense that the obtained optimal order accuracy proves to be similar for both the modified and the original problem.

Reviewer: V.V.Kobkov (Novosibirsk)

### MSC:

65N30 | Finite element, Rayleigh-Ritz and Galerkin 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 |

### Keywords:

finite element method; second-order elliptic interface problems; smooth domains; quasiuniform triangulations
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\textit{J. H. Bramble} and \textit{J. T. King}, Adv. Comput. Math. 6(1996), No. 2, 109--138 (1996; Zbl 0868.65081)

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### References:

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