Explicit numerical methods for the solution of a system of stiff differential equations suffer from a time step size that approaches zero in order to satisfy stability conditions. Implicit schemes allow a larger time-step, but require more computations. When the differential equations are dominated by a skew-symmetric component, the problem is not stiffness in the sense that the size of the eig...

We present a residual based artificial viscosity finite element method to solve conservation laws. The Galerkin approximation is stabilized by only residual based artificial viscosity, without any least-squares, SUPG, or streamline diffusion terms. We prove convergence of the method, applied to a scalar conservation law in two space dimensions, toward an unique entropy solution for implicit tim...

In this paper a combination of discontinuous, piecewise linear, finite elements with implicitexplicit time stepping is considered for convection-reaction equations. Combined with low order quadrature rules, this leads to convenient schemes. We shall consider the effect of such low order quadrature rules on accuracy and stability for one-dimensional problems. 2000 Mathematics Subject Classificat...

During the course of developing new numerical algorithms for a terrain-following ocean modeling system (TOMS), different numerical aspects have been evaluated through a comparison between two widely used community ocean models, the Princeton ocean model (POM) and the regional ocean modeling system (ROMS). While both models aim at modeling coastal to basin-scale problems using similar grids, the...

We consider fully discrete finite element approximations of a Robin optimal boundary control problem, constrained by linear parabolic PDEs with rough initial data. Conforming finite element methods for spatial discretization combined with discontinuous time-stepping Galerkin schemes are being used for the space-time discretization. Error estimates are proved under weak regularity hypotheses for...

This paper presents the development of a 2D high-order solver with spectral difference method for unsteady incompressible Navier–Stokes equations accelerated by a p-multigrid method. This solver is designed for unstructured quadrilateral elements. Time-marching methods cannot be applied directly to incompressible flows because the governing equations are not hyperbolic. An artificial compressib...