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.
Bibliographical noteKAUST Repository Item: Exported on 2022-05-30
Acknowledgements: The first author gratefully acknowledge support by the DFG in the Priority Program SPP 1748 Reliable simulation techniques in solid mechanics, Development of non-standard discretization methods, mechanical and mathematical analysis under the project number BE 6511/1-1. The second author is member of the INdAM Research group GNCS and his research is partially supported by IMATI/CNR and by PRIN/MIUR.
ASJC Scopus subject areas
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics