Name
Abstract | ||
|---|---|---|
A new discontinuous Galerkin finite element method for solving diffusion problems is introduced. Unlike the traditional local discontinuous Galerkin method, the scheme called the direct discontinuous Galerkin (DDG) method is based on the direct weak formulation for solutions of parabolic equations in each computational cell and lets cells communicate via the numerical flux $\widehat{u_x}$ only. We propose a general numerical flux formula for the solution derivative, which is consistent and conservative; and we then introduce a concept of admissibility to identify a class of numerical fluxes so that the nonlinear stability for both one-dimensional (1D) and multidimensional problems are ensured. Furthermore, when applying the DDG scheme with admissible numerical flux to the 1D linear case, $k$th order accuracy in an energy norm is proven when using $k$th degree polynomials. The DDG method has the advantage of easier formulation and implementation and efficient computation of the solution. A series of numerical examples are presented to demonstrate the high order accuracy of the method. In particular, we study the numerical performance of the scheme with different admissible numerical fluxes. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1137/080720255 | SIAM J. Numerical Analysis |
Keywords | Field | DocType |
numerical performance,direct discontinuous galerkin,diffusion problems,finite element method,numerical flux,ddg method,admissible numerical flux,numerical example,ddg scheme,general numerical flux formula,different admissible numerical flux,stability,convergence rate,discontinuous galerkin,diffusion | Discontinuous Galerkin method,Direct method,Mathematical analysis,Finite element method,Rate of convergence,Numerical analysis,Numerical stability,Weak formulation,Mathematics,Numerical linear algebra | Journal |
Volume | Issue | ISSN |
47 | 1 | 0036-1429 |
Citations | PageRank | References |
17 | 1.09 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hailiang Liu | 1 | 88 | 14.62 |
| Jue Yan | 2 | 198 | 24.23 |