Robust Computational Techniques for Various Classes of Singularly Perturbed Problems

Abstract

One of the most common and complex tasks in the field of numerical simulation is the newlineprecise numerical approximation of the interaction between convective and diffusive newlineprocesses that arise in applied sciences and engineering. Boundary layer theory and newlinesingular perturbation problems cover a wide range of ground in this domain. In general, newlinemultiscale phenomena and steep boundary or interior layers are present in the solution newlineof singularly perturbed problems and can be observed in flow experiments. Large newlineoscillations in the solutions are also produced by singularly perturbed problems with newlinehigh Reynolds numbers R or small perturbation parameters and#949;. Furthermore, experiments newlinewith high Reynolds numbers are hardly ever possible. Sometimes singularly perturbed newlineconvection-diffusion problems can be challenging to derive asymptotic solutions to, newlineand it can be challenging to demonstrate with total conviction that the asymptotic newlineapproximations derived are accurate representations of the exact solutions. Consequently, newlineit is essential to know how singularly perturbed convection-diffusion problems with newlineboundary and internal layers are handled numerically and analyzed. newline