A simple adaptive grid method in two dimensions
SIAM Journal on Scientific Computing
Iterative solution methods
Journal of Computational and Applied Mathematics
A Study of Monitor Functions for Two-Dimensional Adaptive Mesh Generation
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
Superconvergence of the Shortley-Weller approximation for Dirichlet problems
Journal of Computational and Applied Mathematics
Convergence of consistent and inconsistent finite difference schemes and an acceleration technique
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
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We are concerned with initial-boundary value problems of convection-diffusion equations in a square, whose solutions have unbounded derivatives near the boundary. By using finite difference approximations with respect to spatial variables and an implicit method with respect to the time variable, it is shown that the numerical solution is convergent if the derivatives go to infinity under proper conditions. Furthermore, the convergence of numerical solution can be accelerated if the mesh points are some functions of equidistant mesh points.