Numerical analysis of dissolution processes in cementitious materials using discontinuous and continuous Galerkin time integration schemes

The present paper is concerned with the numerical integration of non-linear reaction–diffusion problems by means of discontinuous and continuous Galerkin methods. The first-order semidiscrete initial value problem of calcium leaching of cementitious materials, based on a phenomenological dissolution model, an electrolyte diffusion model and the spatial p-finite element discretization, is used as a highly nonlinear model problem. A p-finite element method is used for the spatial discretization. In the context of discontinuous Galerkin methods the semidiscrete mass balance and the continuity of the primary variables are weakly formulated within time steps and between time steps, respectively. Continuous Galerkin methods are obtained by the strong enforcement of the continuity condition as special cases. The introduction of a natural time co-ordinate allows for the application of standard higher order temporal shape functions of the p-Lagrange type and the well-known Gauss–Legendre quadrature of associated time integrals. It is shown, that arbitrary order accurate integration schemes can be developed within the framework of the proposed temporal p-Galerkin methods. Selected benchmark analyses of calcium dissolution demonstrate the robustness of these methods with respect to pronounced changes of the reaction term and non-smooth changes of Dirichlet boundary conditions. Copyright q 2006 John Wiley & Sons, Ltd