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\(hp\)-version discontinuous Galerkin methods for hyperbolic conservation laws. (English) Zbl 0894.76036
Summary: A priori error estimates are derived for a model class of linear hyperbolic conservation laws. These estimates are obtained using a new mesh-dependent norm that reflects the dependence of the approximate solution on the local element size and the local order of approximation. The results generalize and extend previous results on mesh-dependent norms to hp-version discontinuous Galerkin methods. A posteriori error estimates which provide bounds on the actual error are also developed. Numerical experiments verify the a priori estimates and demonstrate the effectiveness of the a posteriori estimates in providing reliable estimates of the actual error in the numerical solution.

76M10 Finite element methods applied to problems in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35L65 Hyperbolic conservation laws
Full Text: DOI
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