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Full-Text Articles in Physical Sciences and Mathematics
Well Conditioned Boundary Integral Equations For Two-Dimensional Sound-Hard Scattering Problems In Domains With Corners, Akash Anand, Jeffrey S. Ovall, Catalin Turc
Well Conditioned Boundary Integral Equations For Two-Dimensional Sound-Hard Scattering Problems In Domains With Corners, Akash Anand, Jeffrey S. Ovall, Catalin Turc
Mathematics and Statistics Faculty Publications and Presentations
We present several well-posed, well-conditioned direct and indirect integral equation formulations for the solution of two-dimensional acoustic scattering problems with Neumann boundary conditions in domains with corners. We focus mainly on Direct Regularized Combined Field Integral Equation (DCFIE-R) formulations whose name reflects that (1) they consist of combinations of direct boundary integral equations of the second-kind and first-kind integral equations which are preconditioned on the left by coercive boundary single-layer operators, and (2) their unknowns are physical quantities, i.e., the total field on the boundary of the scatterer. The DCFIE-R equations are shown to be uniquely solvable in appropriate function …
Reliable A-Posteriori Error Estimators For Hp-Adaptive Finite Element Approximations Of Eigenvalue/Leigenvector Problems, Stefano Giani, Luka Grubisic, Jeffrey S. Ovall
Reliable A-Posteriori Error Estimators For Hp-Adaptive Finite Element Approximations Of Eigenvalue/Leigenvector Problems, Stefano Giani, Luka Grubisic, Jeffrey S. Ovall
Mathematics and Statistics Faculty Publications and Presentations
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.