Optimal a priori estimates for interface problems (Q1412187)

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.