We analyze the optimal global and local convergence properties of continuous Galerkin (CG) solutions on quasi-geometric meshes for delay differential equations with proportional 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 theoretical results are illustrated by a broad range of numerical examples.
Scopus Subject Areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics
- Continuous Galerkin method
- Nonlinear vanishing delay
- Pantograph delay differential equation
- Quasi-geometric mesh