Higher-order discontinuous Galerkin method for pyramidal elements using orthogonal bases

Higher-Order Discontinuous Galerkin Method for Pyramidal Elements using Orthogonal Bases

We study finite elements of arbitrarily high-order defined on pyramids for discontinuous Galerkin methods. We propose a new family of high-order pyramidal finite elements using orthogonal basis functions which can be used in hybrid meshes including hexahedra, tetrahedra, wedges and pyramids. We perform a comparison between these orthogonal functions and nodal functions for affine and non-affine...

High-Order Discontinuous Galerkin Method on Hexahedral Elements for Aeroacoustics High-Order Discontinuous Galerkin Method on Hexahedral Elements for Aeroacoustics

A Discontinuous Galerkin Method for Higher-order Differential Equations

In this paper we propose a new discontinuous finite element method for higher-order initial value problems where the finite element solution exhibits an optimal O(∆tp+1) convergence rate in the L2 norm. We further show that the p-degree discontinuous solution of differential equation of order m and its first m−1 derivatives are O(∆t2p+2−m) superconvergent at the end of each step. We also establ...

Higher order discontinuous Galerkin method for acoustic pulse problem

We discuss the methodology of the validation of a higher order discontinuous Galerkin scheme for acoustic computations. That includes an accurate definition of the exact solution in the problem as well as careful study of convergence properties of a DG scheme for a chosen acoustic problem. The efficiency of a higher order scheme will be confirmed for computations on coarse meshes.

Higher-order Immersed Discontinuous Galerkin Methods

We propose new discontinuous finite element methods that can be applied to one-dimensional elliptic problems with discontinuous coefficients. These methods are based on a class of higher degree immersed finite element spaces and can be used with a mesh independent of the location of coefficient discontinuity. Numerical experiments are presented to show that these methods can achieve optimal con...