On Wavelet-Galerkin Methods for Semilinear Parabolic Equations with Additive Noise
نویسندگان
چکیده
We consider the semilinear stochastic heat equation perturbed by additive noise. After time-discretization by Euler’s method the equation is split into a linear stochastic equation and a non-linear random evolution equation. The linear stochastic equation is discretized in space by a non-adaptive wavelet-Galerkin method. This equation is solved first and its solution is substituted into the nonlinear random evolution equation, which is solved by an adaptive wavelet method. We provide mean square estimates for the overall error.
منابع مشابه
On Wavelet-Galerkin Methods for Semilinear pabolic Equations with Additive Noise
We consider the semilinear stochastic heat equation perturbed by additive noise. After time-discretization by Euler’s method the equation is split into a linear stochastic equation and a non-linear random evolution equation. The linear stochastic equation is discretized in space by a non-adaptive wavelet-Galerkin method. This equation is solved first and its solution is substituted into the non...
متن کاملHp -version Discontinuous Galerkin Finite Element Methods for Semilinear Parabolic Problems
We consider the hp–version interior penalty discontinuous Galerkin finite element method (hp–DGFEM) for semilinear parabolic equations with mixed Dirichlet and Neumann boundary conditions. Our main concern is the error analysis of the hp–DGFEM on shape–regular spatial meshes. We derive error bounds under various hypotheses on the regularity of the solution, for both the symmetric and non–symmet...
متن کاملhp-Version Discontinuous Galerkin Finite Element Method for Semilinear Parabolic Problems
We consider the hp–version interior penalty discontinuous Galerkin finite element method (hp–DGFEM) for semilinear parabolic equations with mixed Dirichlet and Neumann boundary conditions. Our main concern is the error analysis of the hp–DGFEM on shape–regular spatial meshes. We derive error bounds under various hypotheses on the regularity of the solution, for both the symmetric and non–symmet...
متن کاملDuality in Refined Watanabe-sobolev Spaces and Weak Approximations of Spde
In this paper we introduce a new family of refined WatanabeSobolev spaces that capture in a fine way integrability in time of the Malliavin derivative. We consider duality in these spaces and derive a Burkholder type inequality in a dual norm. The theory we develop allows us to prove weak convergence with essentially optimal rate for numerical approximations in space and time of semilinear para...
متن کاملPostprocessing for Stochastic Parabolic Partial Differential Equations
We investigate the strong approximation of stochastic parabolic partial differential equations with additive noise. We introduce post-processing in the context of a standard Galerkin approximation, although other spatial discretizations are possible. In time, we follow [20] and use an exponential integrator. We prove strong error estimates and discuss the best number of postprocessing terms to ...
متن کامل