10 research outputs found
Strong convergence of a fully discrete finite element approximation of the stochastic Cahn-Hilliard equation
We consider the stochastic Cahn-Hilliard equation driven by additive Gaussian
noise in a convex domain with polygonal boundary in dimension . We
discretize the equation using a standard finite element method in space and a
fully implicit backward Euler method in time. By proving optimal error
estimates on subsets of the probability space with arbitrarily large
probability and uniform-in-time moment bounds we show that the numerical
solution converges strongly to the solution as the discretization parameters
tend to zero.Comment: 25 page
A Robust Solver for a Second Order Mixed Finite Element Method for the Cahn-Hilliard Equation
We develop a robust solver for a second order mixed finite element splitting
scheme for the Cahn-Hilliard equation. This work is an extension of our
previous work in which we developed a robust solver for a first order mixed
finite element splitting scheme for the Cahn-Hilliard equaion. The key
ingredient of the solver is a preconditioned minimal residual algorithm (with a
multigrid preconditioner) whose performance is independent of the spacial mesh
size and the time step size for a given interfacial width parameter. The
dependence on the interfacial width parameter is also mild.Comment: 17 pages, 3 figures, 4 tables. arXiv admin note: substantial text
overlap with arXiv:1709.0400
Strong convergence of a fully discrete finite element approximation of the stochastic Cahn-Hilliard equation
We consider the stochastic Cahn-Hilliard equation driven by additive Gaussian noise in a convex domain with polygonal boundary in dimension . We discretize the equation using a standard finite element method is space and a fully implicit backward Euler method in time. By proving optimal error estimates on subsets of the probability space with arbitrarily large probability and uniform-in-time moment bounds we show that the numerical solution converges strongly to the solution as the discretization parameters tend to zero