Partial differential equations -- Numerical solutions, Eigenvalues -- Estimation, Eigenvectors, Boundary value problems
We present reliable a-posteriori error estimates for hp-adaptive finite element approxima- tions of eigenvalue/eigenvector problems. Starting from our earlier work on h adaptive finite element approximations we show a way to obtain reliable and efficient a-posteriori estimates in the hp-setting. At the core of our analysis is the reduction of the problem on the analysis of the associated boundary value problem. We start from the analysis of Wohlmuth and Melenk and combine this with our a-posteriori estimation framework to obtain eigenvalue/eigenvector approximation bounds.
Giani, S., Grubišić, L., & Ovall, J. (2011). Reliable a-posteriori error estimators for $ hp $-adaptive finite element approximations of eigenvalue/eigenvector problems. arXiv preprint arXiv:1112.0436.