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Explore the fundamental differences between standard finite element methods for 3D applications and space-time finite element methods for 4D applications through this seminar presentation from the FEM@LLNL series. Delve into finite element exterior calculus (FEEC) as a framework for understanding these distinctions, utilizing differential geometry and algebraic topology to construct finite element spaces across multiple dimensions. Learn how FEEC techniques enable the construction of derivative operators in both 3D and 4D space, examining the differences between these operators and their associated Sobolev spaces. Discover the construction of conforming, high-order finite element spaces on fundamental 4D geometric shapes including the tesseract, pentatope, and tetrahedral prism, which serve as four-dimensional analogs of the cube, tetrahedron, and triangular prism respectively. Gain insights into advanced computational mathematics and numerical methods through this specialized presentation delivered by David Williams of Penn State University as part of the MFEM project's seminar series focused on finite element research and applications.
