Abstract
The goal of this chapter is to construct vector-valued finite elements to approximate fields with integrable divergence. The finite elements introduced in this chapter can be used, e.g., to approximate Darcy’s equations which constitute a fundamental model for porous media flows. The focus here is on defining a reference element and generating finite elements on the mesh cells. The estimation of the interpolation error is done in Chapters 16 and 17. We detail the construction for the simplicial Raviart–Thomas finite elements. Some alternative finite elements are outlined at the end of the chapter.
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Ern, A., Guermond, JL. (2021). \({{{\varvec{H}}(\text {div})}}\) finite elements. In: Finite Elements I. Texts in Applied Mathematics, vol 72. Springer, Cham. https://doi.org/10.1007/978-3-030-56341-7_14
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DOI: https://doi.org/10.1007/978-3-030-56341-7_14
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Publisher Name: Springer, Cham
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