Discontinuous Galerkin discretization in time of systems of second-order nonlinear hyperbolic equations

Discontinuous Galerkin Finite Element Approximation of Nonlinear Second-Order Elliptic and Hyperbolic Systems

We develop the convergence analysis of discontinuous Galerkin finite element approximations to second-order quasilinear elliptic and hyperbolic systems of partial differential equations of the form, respectively, − ∑d α=1 ∂xαSiα(∇u(x)) = fi(x), i = 1, . . . , d, and ∂2 t ui− ∑d α=1 ∂xαSiα(∇u(t, x)) = fi(t, x), i = 1, . . . , d, with ∂xα = ∂/∂xα, in a bounded spatial domain in R d, subject to mi...

Space-time discontinuous Galerkin discretization of rotating shallow water equations

A space-time discontinuous Galerkin (DG) discretization is presented for the (rotating) shallow water equations over varying topography. We formulate the space-time DG finite element discretization in an efficient and conservative discretization. The HLLC flux is used as numerical flux through the finite element boundaries. When discontinuities are present, we locally apply dissipation around t...

A-stable discontinuous Galerkin-Petrov time discretization of higher order

Discontinuous Galerkin finite element methods for second order hyperbolic problems

In this paper, we prove a priori and a posteriori error estimates for a finite element method for linear second order hyperbolic problems (linear wave equations) based on using spacetime finite element discretizations (for displacements and displacement velocities) with (bilinear) basis functions which are continuous in space and discontinuous in time. We refer to methods of this form as discon...

Wavelet-galerkin Discretization of Hyperbolic Equations

The relative merits of the wavelet-Galerkin solution of hyperbolic partial diieren-tial equations, typical of geophysical problems, are quantitatively and qualitatively compared to traditional nite diierence and Fourier-pseudo-spectral methods. The wavelet-Galerkin solution presented here is found to be a viable alternative to the two conventional techniques.