• Abstract

This article presents an error analysis of a Hermite cubic immersed finite element (IFE) method for solving interface problems of the differential equation modeling a Euler-Bernoulli beam made up of multiple materials together with suitable jump conditions at material interfaces. The analysis consists of three essential groups. The first group is about IFE functions including bounds for the IFE shape functions and inverse inequalities. The second group is about error bounds for IFE interpolation derived with a multi-point Taylor expansion technique. The last group, and perhaps the most important group, is for proving the optimal convergence of the IFE solution generated by the usual Galerkin scheme based on the Hermite cubic IFE space considered in this article.

• Keywords

Error estimation, interface problem, interface independent mesh, Euler-Bernoulli beam, Hermite cubic finite element, multi-point Taylor expansion, optimal convergence

• AMS Subject Headings

65N15, 65N30, 65N50, 35R05.