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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
