We study the mixed formulation of the stochastic Hodge-Laplace problem defined on a n-dimensional domain D (n ≥ 1), with random forcing term. In particular, we focus on the magnetostatic problem and on the Darcy problem in the three dimensional case. We derive and analyze the moment equations, that is the deterministic equations solved by the m-th moment (m ≥ 1) of the unique stochastic solution of the stochastic problem. We find stable tensor product finite element discretizations, both full and sparse, and provide optimal order of convergence estimates. In particular, we prove the inf-sup condition for sparse tensor product finite element spaces.

Moment equations for the mixed formulation of the Hodge Laplacian with stochastic data

BONIZZONI, FRANCESCA;NOBILE, FABIO
2012-01-01

Abstract

We study the mixed formulation of the stochastic Hodge-Laplace problem defined on a n-dimensional domain D (n ≥ 1), with random forcing term. In particular, we focus on the magnetostatic problem and on the Darcy problem in the three dimensional case. We derive and analyze the moment equations, that is the deterministic equations solved by the m-th moment (m ≥ 1) of the unique stochastic solution of the stochastic problem. We find stable tensor product finite element discretizations, both full and sparse, and provide optimal order of convergence estimates. In particular, we prove the inf-sup condition for sparse tensor product finite element spaces.
2012
stochastic PDE; Hodge-Laplace problem; moment equations; sparse tensor product approximation
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/704125
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