Direct discontinuous Galerkin method for nonlinear reaction–diffusion systems in pattern formation

Space-time discontinuous Galerkin method for nonlinear water waves

1 Tankers moored at an oil production center.

Discontinuous Galerkin methods for nonlinear elasticity

A Discontinuous Galerkin Method Applied to Nonlinear Parabolic Equations

Semi-discrete and a family of discrete time locally conservative Dis-continuous Galerkin procedures are formulated for approximations to nonlinear parabolic equations. For the continuous time approximations a priori L 1 (L 2) and L 2 (H 1) estimates are derived and similarly, l 1 (L 2) and l 2 (H 1) for the discrete time schemes. Spatial rates in H 1 and time truncation errors in L 2 are optimal.

A Discontinuous Galerkin Method for Vlasov-Like Systems

This talk will be an amalgamation of aspects of scientific computing – development, verification, and interpretation – with application to the VlasovPoisson (VP) system, an important nonlinear partial differential equation containing the essential difficulties of collisionless kinetic theories. I will describe our development of a discontinuous Galerkin (DG) algorithm,1,2 its verification via c...

A multilevel discontinuous Galerkin method

A variable V-cycle preconditioner for an interior penalty finite element discretization for elliptic problems is presented. An analysis under a mild regularity assumption shows that the preconditioner is uniform. The interior penalty method is then combined with a discontinuous Galerkin scheme to arrive at a discretization scheme for an advection-diffusion problem, for which an error estimate i...