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Optimal a priori error estimates for the \(hp\)-version of the local discontinuous Galerkin method for convection-diffusion problems. (English) Zbl 0997.65111
The paper contains an a priori error estimate for the Galerkin method for one-dimensional convection-diffusion problem with Dirichlet boundary conditions. The error analysis takes into account both the meshsize of the element, \(h\), and the degree of the approximating polynomial in it, \(p\). This method is locally conservative and does not require any inter-element continuity. The results of the paper are some a priori estimates that are optimal both in \(h\) and \(p\).

MSC:
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
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