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On a cell entropy inequality for discontinuous Galerkin methods. (English) Zbl 0801.65098
For the entropy function $$u^ 2/2$$ a cell-by-cell entropy inequality is derived for a class of discrete Galerkin methods for a conservation law. No flux limiter is required. It is also shown that similar entropy inequalities are valid for certain temporal discretizations.

##### MSC:
 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 35L65 Hyperbolic conservation laws
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