Convergence and error analysis for numerical approximations of stochastic Leray-Lions equations
Ngan Le, Huateng Zhu
Source abstract
We analyse a divergence form stochastic differential equation featuring a Leray-Lions flux function that satisfies standard Carathéodory, growth, monotonicity, and coercivity conditions. We consider two types of noise: multiplicative Lipschitz continuous noise and a transport noise. Our approach utilises the gradient discretisation method, a generic framework encompassing various numerical schemes such as conforming and nonconforming finite element methods, hybrid mimetic mixed methods, and hybrid high order methods. For both types of noise, we propose a stable generic scheme, prove that scheme solutions converge to a strong solution in the probabilistic sense. For the multiplicative Lipschitz continuous noise, we establish the rate of convergence.
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