Moment equations for the mixed formulation of the Hodge Laplacian with stochastic loading term
We study the mixed formulation of the stochastic Hodge-Laplace problem dened 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.
2014_Bonizzoni_Buffa_Nobile_IMAJNA_HodgeLapl.pdf
openaccess
343.35 KB
Adobe PDF
ce28f0bf06f95d35651907e8af647f29