Claude Jeffrey Gittelson

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Standard low order Lagrangian finite element discretization of boundary value problems for the Helmholtz equation −∆u−ωu = f are afflicted with the so-called pollution phenomenon: though for sufficiently small hω an accurate approximation of u is possible, the Galerkin procedure fails to provide it. Attempts to remedy this have focused on incorporating(More)
Galerkin 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 = (y1, y2, ...) of possibly countably many parameters yj which are assumed to take values in [−1, 1]. Well-posedness of weak formulations of these parametric equation in suitable(More)