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Optimality of adaptive Galerkin methods for random parabolic partial differential equations
(2013)SAM Research ReportGalerkin discretizations of a class of parametric and random parabolic partial differential equations (PDEs) are considered.The parabolic PDEs are assumed to depend on a vector $y = (y_1,y_2, ...)$ of possibly countably many parameters $y_j$ which are assumed to take values in [−1,1]. Well-posedness of weak formulations of these parametric equation in suitable Bochner spaces is established. Adaptive Galerkin discretizations of the equation ...Report -
Sparse Tensor Approximation of Parametric Eigenvalue Problems
(2010)SAM Research ReportWe design and analyze algorithms for the efficient sensitivity computation of eigenpairs of parametric elliptic self-adjoint eigenvalue problems on high-dimensional parameter spaces. We quantify the analytic dependence of eigenpairs on the parameters. For the efficient approximate evaluation of parameter sensitivities of isolated eigenpairs on the entire parameter space we propose and analyze a sparse tensor spectral collocation method ...Report