In this paper we study the two-dimensional version of the RungeKutta Local Projection Discontinuous Galerkin (RKDG) methods, already defined and analyzed in the one-dimensional case. These schemes are defined on general triangulations. They can easily handle the boundary conditions, verify maximum principles, and are formally uniformly high-order accurate. Preliminary numerical results showing ...

A recent paper [Hideaki Kaneko, Kim S. Bey, Gene J.W. Hou, Discontinuous Galerkin finite element method for parabolic problems, preprint November 2000, NASA] is generalized to a case where the spatial region is taken in R. The region is assumed to be a thin body, such as a panel on the wing or fuselage of an aerospace vehicle. The traditional has well as hp-finite element methods are applied to...

In this paper, we first split the biharmonic equation !2u = f with nonhomogeneous essential boundary conditions into a system of two second order equations by introducing an auxiliary variable v = !u and then apply an hp-mixed discontinuous Galerkin method to the resulting system. The unknown approximation vh of v can easily be eliminated to reduce the discrete problem to a Schur complement sys...

A family of discontinuous Galerkin finite element methods is formulated and analyzed for Stokes and Navier-Stokes problems. An inf-sup condition is established as well as optimal energy estimates for the velocity and L2 estimates for the pressure. In addition, it is shown that the method can treat a finite number of nonoverlapping domains with nonmatching grids at interfaces.

Discontinuous Galerkin (DG) finite element methods were studied by many researchers for second-order elliptic partial differential equations, and a priori error estimates were established when the solution of the underlying problem is piecewise H3/2+ smooth with > 0. However, elliptic interface problems with intersecting interfaces do not possess such a smoothness. In this paper, we establish a...

This paper concerns discontinuous finite element approximations of a fourth-order bi-wave equation arising as a simplified Ginzburg-Landautype model for d-wave superconductors in the absence of an applied magnetic field. In the first half of the paper, we construct a variant of the Morley finite element method, which was originally developed for approximating the fourthorder biharmonic equation...

In this paper we present an error analysis of an Eulerian finite element method for solving parabolic partial differential equations posed on evolving hypersurfaces in Rd, d = 2, 3. The method employs discontinuous piecewise linear in time – continuous piecewise linear in space finite elements and is based on a space-time weak formulation of a surface PDE problem. Trial and test surface finite ...

In this paper we present an error analysis of an Eulerian finite element method for solving parabolic partial differential equations (PDEs) posed on evolving hypersurfaces in Rd, d = 2, 3. The method employs discontinuous piecewise linear in time–continuous piecewise linear in space finite elements and is based on a space-time weak formulation of a surface PDE problem. Trial and test surface fi...