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We propose and analyze sparse deterministic-stochastic tensor Galerkin finite element methods (sparse sGFEMs) for the numerical solution of elliptic partial differential equations (PDEs) with random coefficients in a bounded physical domain D ⊂ R d. The sparse sGFEMs are based on a separation of stochastic and deterministic input variables by Karhunen-Lò(More)
We formulate collocation Runge–Kutta time-stepping schemes applied to linear parabolic evolution equations as space-time Petrov–Galerkin discretizations, and investigate their a priori stability for the parabolic space-time norms, that is the continuity constant of the discrete solution mapping. We focus on collocation based on A-stable Gauss–Legendre and(More)
An attempt was made to test the hypothesis that regular physical activity at the anaerobic threshold can stimulate an increase in the amount of brown or beige body fat, which can manifest itself in increased lactate utilization during exercise and increased reactivity in response to acute regional cooling. The methods used in the study included the ramp(More)
SUMMARY This paper addresses the solution of parabolic evolution equations simultaneously in space and time as may be of interest in e.g. optimal control problems constrained by such equations. As a model problem we consider the heat equation posed on the unit cube in Euclidean space of moderately high dimension. An a priori stable minimal residual(More)
We consider the simultaneous estimation of an optical flow field and an illumination source term in a movie sequence. The particular optical flow equation is obtained by assuming that the image intensity is a conserved quantity up to possible sources and sinks which represent varying illumination. We formulate this problem as an energy minimization problem(More)
We design and analyze algorithms for the efficient sensitivity computation of eigenpairs of parametric elliptic self-adjoint eigenvalue problems (EVPs) on high-dimensional parameter spaces [AS10]. We quantify the analytic dependence of eigen-pairs on the parameters. For the efficient evaluation of parameter sensitivities of isolated eigenpairs on the entire(More)
Galerkin discretizations of a class of parametric and random para-bolic 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(More)
Interconnected lakes Bol’shoe Leprindo and Maloe Leprindo in Transbaikalia hosted large (extinct) and dwarf charr forms. Rarely “small” individuals intermediate in size between these forms are caught. In order to assess morphological, ecological, and genetic differentiation of sympatric charr forms and parapatric charr populations we studied their meristic(More)
Wavelet-in-time multigrid-in-space preconditioning of parabolic evolution equations Powered by TCPDF (www.tcpdf.org) Abstract. Two different space-time variational formulations of linear parabolic evolution equations are considered, one is symmetric and elliptic on the trial space while the other is not. In each case, space-time Petrov–Galerkin(More)