Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4642271 | Journal of Computational and Applied Mathematics | 2008 | 9 Pages |
Abstract
A fully algebraic approach to the design of nonlinear high-resolution schemes is revisited and extended to quadratic finite elements. The matrices resulting from a standard Galerkin discretization are modified so as to satisfy sufficient conditions of the discrete maximum principle for nodal values. In order to provide mass conservation, the perturbation terms are assembled from skew-symmetric internodal fluxes which are redefined as a combination of first- and second-order divided differences. The new approach to the construction of artificial diffusion operators is combined with a node-oriented limiting strategy. The resulting algorithm is applied to P1P1 and P2P2 approximations of stationary convection–diffusion equations in 1D/2D.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Dmitri Kuzmin,