## An immersed finite element space and its approximation capability.(English)Zbl 1057.65085

The authors discuss an immersed finite element space for approximating the solution of interface problems of second-order elliptic partial differential equations. They consider discretizations with triangular elements, where it is allowed that the interface cuts edges of the triangles. On such triangles the finite element functions are defined in such a way that these functions satisfy the jump conditions along the interface. On all other triangles the usual piecewise linear finite element functions are used. Interpolation error estimates for functions in the usual Sobolev spaces are given. The approximation properties of the immersed finite element space are similar to that of the usual finite element space spanned by piecewise linear functions. Finally, numerical experiments are presented which confirm the given error estimates.

### 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
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