The SDFEM for singularly perturbed convection–diffusion problems with discontinuous source term arising in the chemical reactor theory

Abstract

In this paper, we consider singularly perturbed boundary-value problems for second-order ordinary differential equations with discontinuous source term arising in the chemical reactor theory. A parameter-uniform error bound for the solution is established using the streamline-diffusion finite-element method on piecewise uniform meshes. We prove that the method is almost second-order convergence for solution and first-order convergence for its derivative in the maximum norm, independently of the perturbation parameter. Numerical results are provided to substantiate the theoretical results.

Keywords:

• singularly perturbed problem
• discontinuous source term
• streamline-diffusion
• finite-element method
• boundary-value problem

2010 AMS Subject Classifications :

• 65L10
• 65L11
• 65L60