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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.

##### MSC:
 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
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