Mathematics of Computation · 1998 · 119 citations · 16 references
ComputingComputational EngineeringDifferential EquationsFinite Element AnalysisFinite Element MethodsConvergence AnalysisFinite Element DiscretizationFinite Element FormulationNumerical AlgorithmsNumerical AnalysisNumerical Methods For Differential EquationsDiscontinuous Galerkin FormulationFinite Element ModelingGalerkin DiscretizationParabolic Equation ModelingParabolic Partial Differential EquationsTime DiscretizationTime Discretization Error Analysis
The numerical solution of a parabolic equation with memory is considered. The equation is first discretized in time by means of the discontinuous Galerkin method with piecewise constant or piecewise linear approximating functions. The analysis presented allows variable time steps which, as will be shown, can then efficiently be selected to match singularities in the solution induced by singularities in the kernel of the memory term or by nonsmooth initial data. The combination with finite element discretization in space is also studied.
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