2023/08/15 by Jindong Wang, Shuonan Wu, Wang, Jindong +1 · 2 citations
Computer Science · Engineering · #65N12 #65N15 #65N30 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2308.07680
openalex publication_date 2023/08/15 · openalex created_date 2023/08/17 · openalex updated_date 2026/07/28
This paper presents a novel approach to the construction of the lowest order H(curl) and H(div) exponentially-fitted finite element spaces S1-k~(k=1,2) on 3D simplicial mesh for corresponding convection-diffusion problems. It is noteworthy that this method not only facilitates the construction of the functions themselves but also provides corresponding discrete fluxes simultaneously. Utilizing this approach, we successfully establish a discrete convection-diffusion complex and employ a specialized weighted interpolation to establish a bridge between the continuous complex and the discrete complex, resulting in a coherent framework. Furthermore, we demonstrate the commutativity of the framework when the convection field is locally constant, along with the exactness of the discrete convection-diffusion complex. Consequently, these types of spaces can be directly employed to devise the corresponding discrete scheme through a Petrov-Galerkin method.