Some numerical experiments with multigrid methods on Shishkin meshes
Journal of Computational and Applied Mathematics
A Method of Lines Approach to the Numerical Solution of Singularly Perturbed Elliptic Problems
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Multigrid Methods and Finite Difference Schemes for 2D Singularly Perturbed Problems
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Schwarz Methods for Convection-Diffusion Problems
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
A uniformly convergent scheme on a nonuniform mesh for convection-diffusion parabolic problems
Journal of Computational and Applied Mathematics
HODIE finite difference schemes on generalized Shishkin meshes
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
Journal of Computational Physics
A Shishkin mesh for a singularly perturbed Riccati equation
Journal of Computational and Applied Mathematics
An efficient numerical method for singular perturbation problems
Journal of Computational and Applied Mathematics - Special issue on computational and mathematical methods in science and engineering (CMMSE-2004)
A compact finite difference scheme for 2D reaction-diffusion singularly perturbed problems
Journal of Computational and Applied Mathematics - Special issue on computational and mathematical methods in science and engineering (CMMSE-2004)
Journal of Computational and Applied Mathematics - Special issue: The international conference on computational methods in sciences and engineering 2004
Journal of Computational and Applied Mathematics
Using rectangular Qp elements in the SDFEM for a convection--diffusion problem with a boundary layer
Applied Numerical Mathematics
International Journal of Computer Mathematics
Uniform Convergence of Finite-Difference Schemes for Reaction-Diffusion Interface Problems
Large-Scale Scientific Computing
A Shishkin mesh for a singularly perturbed Riccati equation
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Neural, Parallel & Scientific Computations - Special issue on computational techniques for differential equations will applications
Uniform convergence of a monotone iterative method for a nonlinear reaction-diffusion problem
NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
Parallel implementation of a spline based computational approach for singular perturbation problems
HiPC'06 Proceedings of the 13th international conference on High Performance Computing
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Since the first edition of this book, the literature on fitted mesh methods for singularly perturbed problems has expanded significantly. Over the intervening years, fitted meshes have been shown to be effective for an extensive set of singularly perturbed partial differential equations. In the revised version of this book, the reader will find an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. The global errors in the numerical approximations are measured in the pointwise maximum norm. The fitted mesh algorithm is particularly simple to implement in practice, but the theory of why these numerical methods work is far from simple. This book can be used as an introductory text to the theory underpinning fitted mesh methods.