Discontinuous Galerkin Finite Element Method for the Wave Equation.

SIAM Journal on Numerical Analysis (Impact Factor: 1.69). 01/2006; 44:2408-2431. DOI: 10.1137/05063194X
Source: DBLP

ABSTRACT The symmetric interior penalty discontinuous Galerkin nite element method is presented for the numerical discretization of the second-order scalar wave equation. The resulting stiness matrix is symmetric positive denite and the mass matrix is essentially diagonal; hence, the method is inherently parallel and leads to fully explicit time integration. Optimal a priori error bounds are derived in the energy norm and the L2-norm for the semi-discrete formulation. In particular, the error in the energy norm is shown to converge with the optimal orderO(hminfs;'g) with respect to the mesh size h, the polynomial degree ', and the regularity exponent s of the continuous solution. Under additional regularity assumptions, the L2-error is shown to converge with the optimal orderO(h'+1). Numerical results results conrm the expected convergence rates and illustrate the versatility of the method.


Available from: Marcus J. Grote, Feb 01, 2015