Optimal a priori estimates for interface problems. (English) Zbl 1041.65082
The authors study the interface problem for an elliptic operator with piecewise constant diffusion coefficients. They formulate and prove a priori error estimates in weighted norms. They discuss criteria for the existence of a uniform Poincaré estimate in weighted norms. In the affirmative case, a robust finite element error bound in weighted norms is obtained. Finally, numerical experiments are presented including a case with nonuniform Poincaré constant.
Reviewer: Pavel Burda (Praha)
MSC:
65N15 | Error bounds for boundary value problems involving PDEs |
65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
35R05 | PDEs with low regular coefficients and/or low regular data |
35J25 | Boundary value problems for second-order elliptic equations |