Convergence of linear finite elements for diffusion equations with measure data

Approximation of stochastic advection diffusion equations with finite difference scheme

In this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm Ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. We applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. The main properties of deterministic difference schemes,...

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

approximation of stochastic advection diffusion equations with finite difference scheme

in this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. we applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. the main properties of deterministic difference schemes,...

On Multigrid Convergence for Quadratic Finite Elements

Quadratic and higher order finite elements are interesting candidates for the numerical solution of (elliptic) partial differential equations (PDEs) due to their improved approximation properties in comparison to linear approaches. While the systems of equations that arise from the discretisation of the underlying PDEs are often solved by iterative schemes like preconditioned Krylow-space metho...

Convergence rates for adaptive finite elements

In this article we prove that it is possible to construct, using newestvertex bisection, meshes that equidistribute the error in H-norm, whenever the function to approximate can be decomposed as a sum of a regular part plus a singular part with singularities around a finite number of points. This decomposition is usual in regularity results of Partial Differential Equations (PDE). As a conseque...