A Study on Singularly Perturbed Problems under Adaptive Finite Element Framework

Abstract

In this thesis work, robust and efficient adaptive finite element techniques have been proposed for approximating the solutions of singularly perturbed PDEs arising during the analysis of biological systems, heat transfer process, mass transfer process, etc. The research work started with the following three objectives: 1. To propose robust and efficient numerical adaptive finite element technique for linear and non-linear one dimensional singularly perturbed problems. 2. To extend the proposed adaptive techniques (Objective 1) to higher dimensional singularly perturbed problems. 3. To solve some realistic problems arising in various branches of science and engineering. One of the model problems to be considered is Burger Huxley problem. Keeping these objectives in view, the research work has been carried out. These objectives have been achieved via the work which has been categorized into five different Chapters