摘要:

AbstractWe prove a posteriori error estimates for a finite element method for systems of strictly hyperbolic conservation laws in one space dimension, and design corresponding adaptive methods. The proof of the a posteriori error estimates is based on a strong stability estimate for an associated dual problem, together with the Galerkin orthogonality of the finite‐element method. The strong stability estimate uses the entropy condition for the system in an essential way. ©1995 John Wiley&Sons, I

ISSN:0010-3640    

DOI:10.1002/cpa.3160480302

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1995

数据来源: WILEY

摘要:

AbstractWe present a class of numerical schemes (called the relaxation schemes) for systems of conservation laws in several space dimensions. The idea is to use a local relaxation approximation. We construct a linear hyperbolic system with a stiff lower order term that approximates the original system with a small dissipative correction. The new system can be solved by underresolved stable numerical discretizations without using either Riemann solvers spatially or a nonlinear system of algebraic equations solvers temporally. Numerical results for 1‐D and 2‐D problems are presented. The second‐order schemes are shown to be total variation diminishing (TVD) in the zero relaxation limit for scalar equations. ©1995 John Wiley&Son

ISSN:0010-3640    

DOI:10.1002/cpa.3160480303

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1995

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160480304

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1995

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160480301

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1995

数据来源: WILEY