Name
Title | ||
|---|---|---|
A New Nonsymmetric Discontinuous Galerkin Method for Time Dependent Convection Diffusion Equations |
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1007/s10915-012-9637-0 | J. Sci. Comput. |
Keywords | Field | DocType |
baumann-oden method,derivative numerical flux term,diffusion term,linear diffusion problem,numerical example,p k polynomial approximation,solution derivative numerical flux,general nonlinear diffusion equation,new nonsymmetric discontinuous galerkin,convection diffusion equation,numerical solution,time dependent convection diffusion,discontinuous galerkin method,convergence,stability | Convergence (routing),Discontinuous Galerkin method,Order of accuracy,Convection–diffusion equation,Mathematical optimization,Polygon mesh,Mathematical analysis,Test functions for optimization,Finite element method,Piecewise,Mathematics | Journal |
Volume | Issue | ISSN |
54 | 2-3 | 1573-7691 |
Citations | PageRank | References |
1 | 0.38 | 7 |
Authors | ||
1 | ||