Mesh Redistribution Strategies and Finite Element Schemes for Hyperbolic Conservation Laws
- First Online:
- 96 Downloads
In this work we consider a new class of Relaxation Finite Element schemes for hyperbolic conservation laws, with more stable behavior on the limit area of the relaxation parameter. Combining this scheme with an efficient adapted spatial redistribution process considered also in this work, we form a robust scheme of controllable resolution. The results on a number of test problems show that this scheme can produce entropic-approximations of high resolution, even on the limit of the relaxation parameter where the scheme lacks of the relaxation mechanism. Thus we experimentally conclude that the proposed spatial redistribution process, has by its own interesting stabilization properties for computational solutions of conservation law problems.
KeywordsFinite element methods Relaxation model Adaptive mesh redistribution Hyperbolic conservation laws
Unable to display preview. Download preview PDF.
- 4.Babuška, I.: The adaptive finite element method. TICAM Forum Notes no. 7, University of Texas, Austin (1997) Google Scholar
- 7.Billingsley, P.: Probability and Measure, 2nd edn. Wiley, New York (1992) Google Scholar
- 23.Lipnikov, K., Shashkov, M.: The error-minimization-based strategy for moving Mesh methods. Commun. Comput. Phys. 1, 53–81 (2006) Google Scholar
- 30.Tzavaras, A.: Viscosity and relaxation approximation for hyperbolic systems of conservation laws. In: Lecture notes in Computational Science and Engineering, vol. 5, pp. 73–122. Springer, New York (1998) Google Scholar
- 31.Zhang, Z.: Moving mesh methods for convection-dominated equations and nonlinear conservation problems. Ph.D. Thesis, Hong Kong Baptist University (2003) Google Scholar
- 32.Zhang, Z.: Moving mesh method with conservative interpolation based on L 2-projection. Commun. Comput. Phys. 1, 930–944 (2006) Google Scholar