SPRINT2D Software for Convection Dominated PDEs

A discontinuous Galerkin method for optimal control problems governed by a system of convection-diffusion PDEs with nonlinear reaction terms

In this paper, we study the numerical solution of optimal control problems governed by a system of convection diffusion PDEs with nonlinear reaction terms, arising from chemical processes. The symmetric interior penalty Galerkin (SIPG) method with upwinding for the convection term is used for discretization. Residual-based error estimators are used for the state, the adjoint and the control var...

Semi-Lagrangian Runge-Kutta Exponential Integrators for Convection Dominated Problems

In this paper we consider the case of nonlinear convectiondiffusion problems with a dominating convection term and we propose exponential integrators based on the composition of exact pure convection flows. The main reason for developing this type of methods is that as it turns out they can be applied to the numerical integration of the considered PDEs in a semi-Lagrangian fashion. SemiLagrangi...

Parallel Application of a Novel Domain Decomposition Preconditioner for the Stable Finite Element Solution of Three-Dimensional Convection-Dominated PDEs

Parallel application of a novel domain decomposition preconditioner for the adaptive finite-element solution of three-dimensional convection-dominated PDEs

High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments

For solving time-dependent convection-dominated partial differential equations (PDEs), which arise frequently in computational physics, high order numerical methods, including finite difference, finite volume, finite element and spectral methods, have been undergoing rapid developments over the past decades. In this article we give a brief survey of two selected classes of high order methods, n...