Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Journal of Computational Physics
A discontinuous hp finite element method for diffusion problems
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
SIAM Journal on Numerical Analysis
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Journal of Computational Physics
The Direct Discontinuous Galerkin (DDG) Methods for Diffusion Problems
SIAM Journal on Numerical Analysis
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
High Order Finite Difference WENO Schemes for Nonlinear Degenerate Parabolic Equations
SIAM Journal on Scientific Computing
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We propose a discontinuous Galerkin finite element method for convection diffusion equations that involves a new methodology handling the diffusion term. Test function derivative numerical flux term is introduced in the scheme formulation to balance the solution derivative numerical flux term. The scheme has a nonsymmetric structure. For general nonlinear diffusion equations, nonlinear stability of the numerical solution is obtained. Optimal kth order error estimate under energy norm is proved for linear diffusion problems with piecewise P k polynomial approximations. Numerical examples under one-dimensional and two-dimensional settings are carried out. Optimal (k+1)th order of accuracy with P k polynomial approximations is obtained on uniform and nonuniform meshes. Compared to the Baumann-Oden method and the NIPG method, the optimal convergence is recovered for even order P k polynomial approximations.