Energy norm error estimate for singularly perturbed fourth-order differential equation with two parameters

We consider a fourth-order reaction-diffusion-type singularly perturbed boundary value problem with two small parameters epsilon(1) and epsilon(2) multiplied to the fourth- and second-order derivative terms respectively. In this article, we restrict to a special case, where epsilon(1) << epsilon(2) and derive the finite element scheme using Ritz-Galerkin finite element method with lumping process. On discretizing the domain, the layer-adapted meshes like Standard-Shishkin, Bakhvalov-Shishkin and Modified-Bakhvalov-type meshes and piecewise quadratic polynomials are used and the error estimates are derived in L-2-norm and energy norm. The numerical experiments given in the article supports these theoretical findings.