# Numerical Solution of Singularly Perturbed Problems via both Galerkin and Subdomain Galerkin methods

## TL;DR

This paper presents numerical solutions for singularly perturbed boundary value problems using Galerkin and subdomain Galerkin finite element methods with quadratic B-splines, demonstrating their effectiveness through comparison with analytical solutions.

## Contribution

It introduces the application of quadratic B-spline based Galerkin and subdomain Galerkin methods to singularly perturbed problems on graded meshes, providing new insights into their accuracy.

## Key findings

- Methods accurately approximate analytical solutions
- Subdomain Galerkin method improves convergence
- Effective for problems with boundary layer behavior

## Abstract

In this paper, numerical solutions of singularly perturbed boundary value problems are given by using variants of finite element method. Both Galerkin and subdomain Galerkin method based on quadratic B-spline functions are applied over the geometrically graded. Results of some text problems are compated with analytical solutions of the singularly perturbed problem