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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)

An approximate error function for the discretization error on a given mesh is obtained by projecting (via the energy inner product) the functional residual onto the space of continuous, piecewise quadratic functions which vanish on the vertices of the mesh. Conditions are given under which one can expect this hierarchical basis error estimator to give… (More)

We present several well-posed, well-conditioned integral equation formulations for the solution of two-dimensional acoustic scattering problems with Neumann boundary conditions in domains with corners. We call these integral equations Direct Regularized Combined Field Integral Equations (DCFIE-R) formulations because (1) they consist of combinations of… (More)

As a model benchmark problem for this study we consider a highly singular transmission type eigenvalue problem which we study in detail both analytically as well as numerically. In order to justify our claim of cluster robust and highly accurate approximation of a selected groups of eigenvalues and associated eigenfunctions, we give a new analysis of a… (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)

- Jeffrey Ovall, Kerry Key, J. Ovall
- 2011

SUMMARY We present a parallel goal-oriented adaptive finite element method that can be used to rapidly compute highly accurate solutions for 2.5D controlled-source electromagnetic (CSEM) and 2D magnetotelluric (MT) modeling problems. We employ unstructured triangular grids that permit efficient discretization of complex modeling domains such as those… (More)

- JEFFREY S. OVALL
- 2004

Let S = {x 1 , x 2 ,. .. , xn} be a set of distinct positive integers such that gcd(x i , x j) ∈ S for 1 ≤ i, j ≤ n. Such a set is called GCD-closed. In 1875/1876, H.J.S. Smith showed that, if the set S is " factor-closed " , then the determinant of the matrix e ij = gcd(x i , x j) is det(E) = n m=1 φ(xm), where φ denotes Euler's Phi-function. Since the… (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)