Discrete and Continuous Dynamical Systems · 2016 · 20 citations · 16 references
ComputingComputational EngineeringMathematicsDifferential EquationsFinite Element AnalysisFinite Element MethodsConvergence AnalysisFinite Element DiscretizationFinite Element FormulationMesh AnalysisMesh GenerationNumerical Methods For Differential EquationsConvergence Under Mesh RefinementDelay EquationsGalerkin DiscretizationLocal Convergence AnalysisMesh ConvergenceMesh Convergence AnalysisSuperconvergence
We analyze the optimal global and local convergence properties of continuous Galerkin (CG) solutions on quasi-geometric meshes for delay differential equations withproportional delay. It is shown that with this type of meshes the attainable order of nodal superconvergence of CG solutions is higher than of the one for uniform meshes. The theoreticalresults are illustrated by a broad range of numerical examples.
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