A continuous interior penalty finite element method for a third-order singularly perturbed boundary value problem

Abstract

© 2016, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional. We propose a continuous interior penalty finite element method designed for a third-order singularly perturbed problem. Using higher order polynomials on Shishkin-type layer-adapted meshes, a robust convergence has been proved in the corresponding energy norm. Moreover, we show numerical experiments which support our theoretical findings.