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Description

Partial Differential Equations Seminar.

Speaker: Pratibhamoy Das

Affiliation: IIT Patna

Date and Time: Wednesday 13 March, 4.00 pm - 5.00 pm

Venue: Room 216, Department of Mathematics.

Title: A Priori and A Posteriori Based Parameter Uniform Convergence
Analysis for Solutions of Singularly Perturbed Differential Equations.

Abstract: Singular perturbation and the boundary layer phenomena appear
very often in several applications today. Presence of a small parameter in
the differential equation changes the behavior of the solution rapidly.
Uniform meshes are inadequate for the convergence of numerical solution.
The aim of the present talk is to consider the adaptive mesh generation
for these problems based on moving mesh strategy.

I shall start this talk with a small introduction on singular
perturbation. The analytical and computational difficulties in the existed
methods will be discussed. The concept of moving mesh strategy and its
implementation will be explained. A nonlinear system of differential
equations with delay will be considered to show the difference between a
priori and a posteriori generated meshes after discussing my researches on
this field. The parameter uniform a posteriori based error estimate for a
system of reaction-diffusion problems and a priori based convergence
analysis for a parabolic convection-diffusion problem will be presented
with computational evidence.

Pratibhamoy Das, IIT Patna