Academic Journal
Superconvergence of Discontinuous Galerkin Solutions for a Nonlinear Scalar Hyperbolic Problem
| العنوان: | Superconvergence of Discontinuous Galerkin Solutions for a Nonlinear Scalar Hyperbolic Problem |
|---|---|
| المؤلفون: | Adjerid, Slimane, Massey, Thomas C. |
| المساهمون: | NAVAL RESEARCH LAB STENNIS SPACE CENTER MS OCEANOGRAPHY DIV |
| المصدر: | DTIC |
| سنة النشر: | 2006 |
| المجموعة: | Defense Technical Information Center: DTIC Technical Reports database |
| مصطلحات موضوعية: | Numerical Mathematics, Fluid Mechanics, CONVERGENCE, DISCONTINUITIES, HYPERBOLAS, GALERKIN METHOD, REPRINTS, FLUX(RATE), SCALAR FUNCTIONS, CONSERVATION, NONLINEAR ANALYSIS, FINITE ELEMENT ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, SUPERCONVERGENCE, DG(DISCONTINUOUS GALERKIN), PE0602435N, 73-6801-85 |
| الوصف: | 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(h p+2) rate. We further show that the solution flux converges on average at O(h 2p+2)) on element outflow boundary when no reaction terms are present. Globally, we prove that the flux converges at O(h 2p+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. ; Published in Computer Methods in Applied Mechanics and Engineering, v195 p3331-3346, 2006. Prepared in collaboration with Virginia Polytechnic Institute and State University, Blacksburg, VA. |
| نوع الوثيقة: | text |
| وصف الملف: | text/html |
| اللغة: | English |
| Relation: | http://www.dtic.mil/docs/citations/ADA449226 |
| الاتاحة: | http://www.dtic.mil/docs/citations/ADA449226 http://oai.dtic.mil/oai/oai?&verb=getRecord&metadataPrefix=html&identifier=ADA449226 |
| Rights: | Approved for public release; distribution is unlimited. |
| رقم الانضمام: | edsbas.23650BD6 |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |