Jeffrey S. Ovall

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We consider a large class of residuum based a posteriori eigen-value/eigenvector estimates and present an abstract framework for proving their asymptotic exactness. Equivalence of the estimator and the error is also established. To demonstrate the strength of our abstract approach we present a detailed study of hierarchical error estimators for Laplace(More)
We present a new algorithm, based on integral equation formulations, for the solution of constant-coefficient elliptic partial differential equations (PDE) in closed two-dimensional domains with non-smooth boundaries; we focus on cases in which the integral-equation solutions as well as physically meaningful quantities (such as, stresses, electric/magnetic(More)
In this paper, we investigate the effects of pollution error on the performance of the parallel adaptive finite element technique proposed by Bank and Holst in 2000. In particular, we consider whether the performance of the algorithm as it was originally proposed can be improved through the use of certain dual functions which give indication of global(More)
We consider a two-level block Gauss-Seidel iteration for solving systems arising from finite element discretizations employing higher-order elements. A p-hierarchical basis is used to induce this block structure. Using superconvergence results normally employed in the analysis of gradient recovery schemes, we argue that a massive reduction of H 1-error(More)
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(More)
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