| Abstract: |
| Extending the stochastic generalization of the variational framework originally developed for deterministic multisymplectic partial differential equations, we introduce a stochastic variational formulation that guarantees the preservation of stochastic 1-form and 2-form conservation laws, together with stochastic counterparts of Noether`s theorem. Motivated by this formulation, we develop a family of stochastic collocation schemes that inherently preserve geometric structure. In particular, these methods maintain the stochastic multisymplectic 2-form at the discrete level. For linear problems, the proposed approach additionally ensures the preservation of discrete momentum. |
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