Discontinuous Petrov–Galerkin Approximation of Eigenvalue Problems

Abstract

Abstract In this paper, the discontinuous Petrov–Galerkin approximation of the Laplace eigenvalue problem is discussed. We consider in particular the primal and ultraweak formulations of the problem and prove the convergence together with a priori error estimates. Moreover, we propose two possible error estimators and perform the corresponding a posteriori error analysis. The theoretical results are confirmed numerically, and it is shown that the error estimators can be used to design an optimally convergent adaptive scheme.