کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
499933 | 863066 | 2006 | 16 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Superconvergence of discontinuous Galerkin solutions for a nonlinear scalar hyperbolic problem Superconvergence of discontinuous Galerkin solutions for a nonlinear scalar hyperbolic problem](/preview/png/499933.png)
In this paper we study the superconvergence of the discontinuous Galerkin solutions for nonlinear hyperbolic partial differential equations. On the first inflow element we prove that the p-degree discontinuous finite element solution converges at Radau points with an O(hp+2) rate. We further show that the solution flux converges on average at O(h2p+2) on element outflow boundary when no reaction terms are present. For reaction–convection problems we establish an O(hmin(2p+2,p+4)) superconvergence rate of the flux on element outflow boundary. Globally, we prove that the flux converges at O(h2p+1) on average at the outflow of smooth-solution regions for nonlinear conservation laws. Numerical computations indicate that our results extend to nonrectangular meshes and nonuniform polynomial degrees. We further include a numerical example which shows that discontinuous solutions are superconvergent to the unique entropy solution away from shock discontinuities.
Journal: Computer Methods in Applied Mechanics and Engineering - Volume 195, Issues 25–28, 1 May 2006, Pages 3331–3346