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An unfitted finite element method, based on Nitsche’s method, for elliptic interface problems. (English) Zbl 1035.65125
A method or the finite element solution of an elliptic interface problem is given which uses J. Nitsche’s method [Abh. Math. Semin. Univ. Hamb. 36, 9–15 (1971; Zbl 0229.65079)]. It allows for discontinuities internal to the elements. The optimal order of convergence holds without restrictions on the location of the interface relative to the mesh. A posteriori error estimates for controlling functionals are derived.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer
35J25 Boundary value problems for second-order elliptic equations
65N15 Error bounds for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
80A20 Heat and mass transfer, heat flow (MSC2010)
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