Evaluating the solution accuracy of the heat equation by a posteriori error estimation

Abstract

A produce based on a guaranteed posterior error estimates is proposed to estimate the accuracy of solution of the time-dependent heat equation. The time-dependent heat equation is discretized by the backward Euler scheme in time and conforming finite elements in space. The error between the exact solution and the numeric solution in space is bounded by a guaranteed posterior error estimates which is calculated at every time step. Numerical results demonstrate that the produce can be used to evaluate the accuracy of numerical solutions.