Adaptive Finite Element Methods for Reactive Flow Problems

We present and analyze adaptive finite element methods with reliable and efficient error control for a variety of convection-diffusion-reaction problems. The adaptive methods are based on a posteriori error estimates, where the error is estimated in terms of the residual of the computed solution, the mesh size and multiplicative factors measuring certain stability properties of an associated linearized dual problem. The stability factors are computed numerically by solving the linearized dual problem. We present several computational examples illustrating applications to reaction-diffusion problems and reactive compressible flow