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Compatible Finite Elements for Problems in Mixed Form

In this lecture we will analyze several model problems of physical importance (such as Poisson, Stokes and Maxwell equations), and their approximation by mixed finite element methods. By expressing them in the framework of Hilbert complexes we will better understand some guiding principles of compatible finite element methods which preserve their structure at the discrete level. In particular, we will see how some key stability and accuracy properties of compatible finite element methods derive from this structure. By reviewing some important examples based on spline and spectral finite element spaces, students will be able to derive by themselves the building blocks of such compatible finite element methods.

Compatible finite element methods (FEM) are frequently used in the context of plasma physics simulations.

Until further notice, the lecture will be given online (details below).

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-- MartinCamposPinto - 11 June 2021