An a posteriori estimator of eigenvalue/eigenvector error for penalty-type discontinuous Galerkin methods

摘要: We provide an abstract framework for analyzing discretization error eigenvalue problems discretized by discontinuous Galerkin methods such as the local method and symmetric interior penalty method. The analysis applies to clusters of eigenvalues that may include degenerate eigenvalues. use asymptotic perturbation theory linear operators analyze dependence eigenspaces on parameter. first formulate DG in quadratic forms construct a companion infinite dimensional problem. With problem, eigenvalue/vector is estimated sum two components. component can be viewed “non-conformity” we argue neglected practical estimates properly choosing second posteriori using auxiliary subspace techniques, this constitutes estimate.