Numerical Analysis of Diffusion and Heat Conduction Problems by Means of Discontinuous Galerkin Methods in Space and Time

The presentation is concerned with the numerical treatment of transient transport problems like heat transfer or mass/species transport by means of discontinuous spatial discretization and different time integration schemes. To achieve a semidiscrete initial value problem discontinuous -finite elements for the approximation in space are used, where the continuity at the interelement boundaries is just weakly enforced. Furthermore, continuous and discontinuous Galerkin time integration schemes, which evaluate the balance equation in a weak sense over the time interval, are presented. These discretization techniques are investigated with respect to robustness, reliability and accuracy, also in the context of non-smooth initial or boundary conditions. Selected benchmark analyses of heat conduction with an available analytical solution are analyzed for the above described numerical methods. Moreover the highly non-linear reaction-diffusion process of calcium leaching in cementitious materials, which has a major influence on the durability of concrete structures, is modeled by means of the Theory of Porous Media and simulated by spatial and temporal finite element methods.