@misc{KornhuberWittum, author = {Kornhuber, Ralf and Wittum, Gabriel}, title = {Discretization and Iterative Solution of Convection Diffusion Equations.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-762}, number = {SC-92-06}, abstract = {We propose an extended box method which turns out to be a variant of standard finite element methods in the case of pure diffusion and an extension of backward differencing to irregular grids if only convective transport is present. Together with the adaptive orientation proposed in a recent paper and a streamline ordering of the unknowns, this discretization leads to a highly efficient adaptive method for the approximation of internal layers in the case of large local Peclet numbers.}, language = {en} } @misc{NaegelDeuflhardWittum, author = {N{\"a}gel, Arne and Deuflhard, Peter and Wittum, Gabriel}, title = {Efficient Stiff Integration of Density Driven Flow Problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-70891}, abstract = {The paper investigates the efficient use of a linearly implicit stiff integrator for the numerical solution of density driven flow problems. Upon choosing a one-step method of extrapolation type (code LIMEX), the use of full Jacobians and reduced approximations are discussed. Numerical experiments include nonlinear density flow problems such as diffusion from a salt dome (2D), a (modified) Elder problem (3D), the saltpool benchmark (3D) and a real life salt dome problem (2D). The arising linear equations are solved using either a multigrid preconditioner from the software package UG4 or the sparse matrix solver SuperLU.}, language = {en} }