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A posteriori error estimates for a finite element approximation of transmission problems with sign changing coefficients. (English) Zbl 1220.65167

The authors consider a Galerkin approximation for a Dirichlet problem attached to a second order divergence type equation with sign changing coefficients. The lack of the coerciveness is the key point in this analysis. They prove the well-posedness of the discrete approximation and carry out an a posteriori error analysis provided that the contrast, i.e., the ratio between the min of positive “part” of the coefficient and the max of the absolute value of the negative “part”, is large enough. Two numerical examples (a polynomial and a singular solution) are considered in order to illustrate the theoretical predictions.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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