Reconstructing algebraic functions from a nonconforming exponential weighted enriched finite element

The reconstruction of functions is a fundamental task in various applications, ranging from computer graphics to remote sensing. This paper addresses the challenge of function reconstruction in scenarios where, instead of pointwise function evaluations, only a set of integrals over specific lines is available. We propose a novel method based on a one-parameter family of weighted finite elements that incorporates exponential Hermite weight functions within bounded domains. Numerical experiments demonstrate that the proposed approach significantly improves computational efficiency and accuracy in function reconstruction compared to the classical Crouzeix–Raviart finite element.