Exponentially-fitted finite elements for H( curl) and H( div) convection-diffusion problems
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This paper presents a novel approach to the construction of the lowest order H(curl) and H(div) exponentially-fitted finite element spaces 𝒮_1^-^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.
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