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arXiv · 1604.06611

Quasi-optimality of Petrov-Galerkin discretizations of parabolic problems with random coefficients

Stig Larsson·Christian Mollet·Matteo Molteni
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Abstract

We consider a linear parabolic problem with random elliptic operator in the usual Gelfand triple setting. We do not assume uniform bounds on the coercivity and boundedness constants, but allow them to be random variables. The parabolic problem is studied in a weak space-time formulation, where we can derive explicit formulas for the inf-sup constants. Under suitable assumptions we prove existence of moments of the solution. We also prove quasi-optimal error estimates for piecewise polynomial Petrov-Galerkin discretizations.

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Stig Larsson, Christian Mollet, Matteo Molteni. 2016-04-22. Quasi-optimality of Petrov-Galerkin discretizations of parabolic problems with random coefficients. https://arxiv.org/abs/1604.06611

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