Two-dimensional fully adaptive solutions of reaction-diffusion equations Original Research Article

We present an adaptive Rothe method for two-dimensional problems combining an embedded Runge-Kutta scheme in time and a multi-level finite element discretization in space. The spatial discretization error is controlled by a posteriori error estimates based on interpolation techniques. A computational example for a thermodiffusive flame propagation model illustrates the high accuracy that is possible with the proposed method.