Analytical and Numerical Methods for Convection-dominated and Singularly Perturbed ProblemsThis volume is the Proceedings of the Workshop on Analytical and Computational Methods for Convection-Dominated and Singularly Perturbed Problems, which took place in Lozenetz, Bulgaria, 27-31 August 1998. The workshop attracted about 50 participants from 12 countries. The volume includes 13 invited lectures and 19 contributed papers presented at the workshop and thus gives an overview of the latest developments in both the theory and applications of advanced numerical methods to problems having boundary and interior layers. There was an emphasis on experiences from the numerical analysis of such problems and on theoretical developments. The aim of the workshop was to provide an opportunity for scientists from the East and the West, who develop robust methods for singularly perturbed and related problems and also who apply these methods to real-life problems, to discuss recent achievements in this area and to exchange ideas with a view of possible research co-operation. |
Contents
Numerical Solution of Singularly Perturbed Boundary Value Problems with Power and Logarithmic Boundary Layers | 15 |
A Combined Finite Difference and Local Method of Characteristic Line Approximation for ConvectionDiffusion Problems | 2 |
Singularly perturbed differential equations with discontinuous source terms | 21 |
Schwartz Methods for Singularly Perturbed ConvectionDiffusion Problems | 31 |
Parallel Methods Based on a DefectCorrection Technique for Parabolic Singularly Perturbed Problems | 41 |
Finite Element Method with Fitted Integration Rule for ConvectionDiffusion Problem with Small | 49 |
Gradient BlowingUp Phenomenon for Solutions to Parabolic Problems | 57 |
Error control local grid refinement and efficient solution algorithms for singularly perturbed problems | 69 |
Singularly Perturbed ConvectionDiffusion Parabolic Problem with Concentrated Capacity | 159 |
Numerical Solution of DiffusionDesorbtion Problems with Small Diffusion Coefficients and Localized Chemical Reactions | 167 |
Fourth Order Alternating Direction Methods For Evolutionary ConvectionDiffusion Problems | 175 |
Iterative Solution of Steady ConvectionDiffusion Equation with Dominant Convection | 183 |
Some superconvergence results for finite element discretizations on a Shishkin mesh of a convectiondiffusion problem | 191 |
A Novel ShishkinType Mesh for ConvectionDiffusion Problems | 197 |
Fitted Mesh Collocation Techniques For Solution of Adsorption Problems in Bidisperse Solids | 203 |
Schwarz iterative method for convectiondiffusion problems with boundary layers | 211 |
Leastsquares streamline diffusion finite element approximations to singularly perturbed convectiondiffusion problems | 81 |
Grid Generation Based on Analysis of Singular Equations | 93 |
Nonlinear Monotone Difference Schemes for the Transport Equation | 103 |
Approximation of Singularly Perturbed ConvectionDiffusion Equations with Low Smoothness of the Derivatives Involved in the Equation | 109 |
Convergence Properties of the StreamlineDiffusion Finite Element Method on a Shishkin Mesh for Singularly Perturbed Elliptic Equations with Expo... | 121 |
Uniform with respect to a Small Parameter Convergence of Difference Schemes for a ConvectionDiffusion Problem | 131 |
Generalized Point Model of a Narrow Crack in a Fluid Loaded Elastic Plate | 139 |
The Additive Extraction Method for Singular Perturbation Problems | 145 |
Asymptotics for the Grid Approximations of the Singular Solutions of the Boundary Value Problems for the Laplace Equation in a Sector | 153 |
A parameter robust numerical method for a system of singularly perturbed ordinary differential equations | 217 |
Multigrid Method for ConvectionDiffusion Problem with Dominant Convection | 223 |
Convection Oriented Scheme for Twodimensional Singularly Perturbed Problems | 229 |
Analysis of Nonlinear Damped Vibrations of a TwoDegreeofFreedom Mechanical System by Use of Fractional Calculus | 241 |
A Decomposition Method for Quasilinear Singularly Perturbed Parabolic Equations in the ReactionDiffusion Case | 249 |
| 257 | |
A FEM for Singularly Perturbed Diffusion Problems with Discontinuous Coefficients and Concentrated Factors | 263 |
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Common terms and phrases
accuracy analysis applied approximation assume basic boundary conditions boundary layer boundary value problem bounded coefficients components computed consider constant constructed continuous convection Convection-Diffusion Problems convergence corresponding defined denote dependent derivative difference scheme differential equations diffusion direction discrete domain elliptic equation error estimate exact example Figure finite difference finite element method fitted function given gives grid holds interior interval introduce iterative Lemma linear Math matrix maximum Miller monotone nodes nonlinear norm Note numerical methods numerical solution obtained operator parabolic equations parameter piecewise points positive presented Proof proved refinement regular respect Russian satisfies shows singular singularly perturbed singularly perturbed problems small parameter smooth solution solving space standard sufficiently Table technique Theorem uniform mesh