Error control for \(hp\)-adaptive approximations of semi-definite eigenvalue problems
We present reliable \(\alpha \)-posteriori error estimates for \(hp\)-adaptive finite element approximations of semi-definite eigenvalue/eigenvector problems. Our model problems are motivated by applications in photonic crystal eigenvalue computations. We present detailed numerical experiments confirming our theory and give several benchmark results which could serve the purpose of numerical testing of other adaptive procedures.
eigenvalue problem finite element method a posteriori error estimates primary 65n30 secondary 65n25 65n15