Speaker: Shuonan Wu, Assistant Professor, Peking University

Inviter: Wei Gong, Associate Professor

Title: Exponentially-fitted Finite Elements for H(curl) and H(div) Convection-Diffusion Problems

Time & Venue: 2024.04. 23 10:00-11:00, N219

Abstract: This talk presents a novel approach to the construction of the lowest order H(curl) and H(div) exponentially-fitted finite element spaces 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.