Quadrature-Free Implementation of the Discontinuous Galerkin Method for Hyperbolic EquationsA discontinuous Galerkin formulation that avoids the use of discrete quadrature formulas is described and applied to linear and nonlinear test problems in one and two space dimensions. This approach requires less computational time and storage than conventional implementations but preserves the compactness and robustness inherent to the discontinuous Galerkin method. Test problems include both linear and nonlinear one-dimensional scalar advection of botH smooth and discontinuous initial value problems, two-dimensional scalar advection of smooth initial value problems discretized by using unstructured grids with varying degrees of smoothness and regularity, and two-dimensional linear Euler solutions on unstructured grids.
Document ID
19960025087
Acquisition Source
Langley Research Center
Document Type
Conference Paper
Authors
Atkins, H. L. (NASA Langley Research Center Hampton, VA United States)
Shu, Chi-Wang (Brown Univ. Providence, RI United States)