# Accelerated finite elements schemes for parabolic stochastic partial differential equations

## TL;DR

This paper demonstrates how Richardson extrapolation can accelerate the convergence rate of finite element schemes for linear stochastic parabolic PDEs, given smooth data and coefficients.

## Contribution

It introduces a method to enhance convergence speed of finite element approximations for stochastic parabolic PDEs through Richardson extrapolation.

## Key findings

- Accelerated convergence rates achieved with Richardson extrapolation.
- Applicable to smooth coefficients and data.
- Convergence can be arbitrarily fast with proper mixture of approximations.

## Abstract

For a class of finite elements approximations for linear stochastic parabolic PDEs it is proved that one can accelerate the rate of convergence by Richardson extrapolation. More precisely, by taking appropriate mixtures of finite elements approximations one can accelerate the convergence to any given speed provided the coefficients, the initial and free data are sufficiently smooth.