On some aspects of the discontinuous Galerkin finite element method for conservation laws

2003 ◽  
Vol 61 (3-6) ◽  
pp. 333-346 ◽  
Author(s):  
Vít Dolejší ◽  
Miloslav Feistauer ◽  
Christoph Schwab
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Conservation Laws ◽  
Discontinuous Galerkin ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Discontinuous Galerkin Finite Element ◽  
Element Method

CONVERGENCE OF THE DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR HYPERBOLIC CONSERVATION LAWS

1995 ◽  
Vol 05 (03) ◽  
pp. 367-386 ◽  
Author(s):  
J. JAFFRE ◽  
C. JOHNSON ◽  
A. SZEPESSY
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Conservation Laws ◽  
Discontinuous Galerkin ◽  
Hyperbolic Conservation Laws ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Discontinuous Galerkin Finite Element ◽  
Systems Of Conservation Laws ◽  
Element Method

We prove convergence of the discontinuous Galerkin finite element method with polynomials of arbitrary degree q≥0 on general unstructured meshes for scalar conservation laws in multidimensions. We also prove for systems of conservation laws that limits of discontinuous Galerkin finite element solutions satisfy the entropy inequalities of the system related to convex entropies.

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