Gravity seminar - Kaibo Hu (Oxford) Seminar

Abstract: In computational electromagnetism, the de Rham complex encodes crucial structures of the Maxwell equations. Preserving these structures is important for the construction of reliable numerical methods. This cohomological perspective has been developed into the framework of Finite Element Exterior Calculus (FEEC). In this talk, we review the basic ideas of FEEC, and investigate other complexes with applications in continuum mechanics, differential geometry and general relativity. The Bernstein-Gelfand-Gelfand (BGG) machinery implies algebraic and analytic results of such complexes. In particular, these complexes provide a parametrisation of the linearised constraint equations in relativity.