| Abstract: |
| We study an approximation by a finite-volume scheme in space and a semi-implicit discretization in time for a stochastic heat equation with convection and a multiplicative Lipschitz noise.
In the passage to the limit the main difficulty is to identify the limit of the non-linear terms.
In the special case of a heat equation without convection we use a stochastic compactness method based on Skorokhod's representation theorem to get first a martingale solution and then, by a pathwise uniqueness argument, the unique variational solution.
In the general case with convection we are able to prove convergence of the scheme adapting well-known monotonicity methods to the stochastic framework. |
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