A generalized quadrature free discontinuous Galerkin method

Abstract

This chapter introduces a quadrature free discontinuous Galerkin method using a general polynomial basis set. The generalized method allows one to use a basis set made up of any polynomial function, without the use of quadrature to evaluate the integrals of the discontinuous Galerkin formulation. This allows the use of polynomials— such as Lagrange, Jacobi or similar polynomials whose properties considerably reduce the computation time required for boundary integrals. With the use of a Lagrange polynomial basis set, the nonlinear flux terms are shown to be expanded easily. The discontinuous Galerkin method (DG method) has been extensively developed over the past decade to seek solutions in many fields such as computational aeroacoustics, compressible fluid dynamics, and electromagnetics.