Project Grant 2208551

This three-year, $237,648 Project Grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) will support the development of structure-preserving hybrid finite element methods. The principal investigator will investigate techniques for capturing fundamental physical laws like conservation and dissipation within simulations performed using finite element methods. Specifically, the research will focus on circumventing barriers to local structure preservation through hybridization. This includes extending hybrid methods to systems where a quadratic quantity is dissipated rather than conserved. The award will also enable investigation of applying hybrid finite element exterior calculus methods to Hamiltonian partial differential equations, with a focus on multisymplectic structure preservation and hybridizable discontinuous Galerkin methods with strongly conservative fluxes. Outcomes of this research could lead to new computational methods and improved understanding of current approaches, benefiting computational physics and engineering applications. Work will be performed at Washington University in University City, Missouri.