A posteriori error analysis for a fully discrete discontinuous Galerkin approximation to a kind of reactive transport problems

Abstract

In order to obtain an expected numerical solution, a fully discrete discontinuous Galerkin method is applied to a kind of reactive transport problems in two dimension. That is to say, the space variable is discretized with the symmetric interior penalty Galerkin method (SIPG), and the time variable is done with the backward Euler method. Making use of the duality technique, hp approximation properties and the interpolation theory, a residual-type a posteriori error estimation is achieved, which can be used for adaptivity. Compared with the analyses of semi-discretization, the current presentation is more challenging and more significant.