The finite element method (FEM) was introduced by engineers [1] for the solution of partial differential equations (PDEs) and analyzed later, for example, by Ciarlet [2].

In this paper, the authors use the Galerkin FEM to solve a fourth-order time-independent PDE with Dirichlet (given solution on the boundary) and Neumann (given value of the normal derivative) boundary conditions in 2D and 3D domains. This model problem arises from fluorescence tomography (FT). “Fluorescence tomography imaging (FTI) has emerged as a highly sensitive molecular imaging technology capable of spatially resolving the concentration of targeted and activated fluorescent agents located deep in soft tissue” [3]. The authors introduced the variational (weak) formulation of the problem. The nonconforming finite elements [4] used for this problem are different from what has been used before. They derive and prove an error estimate. Several numerical experiments are described, demonstrating the performance of the method and validating the optimal order of convergence proven.