Superconvergent Finite Element Solutions To Einstein's Constraint Equations On Multi-block Triangulations

Abstract

I will present an approach for solving Einstein's constraint equations on three-dimensional multi-block domains using finite element methods. The solution, obtained using quadratic Lagrange elements on semi-structured simplicial meshes, appears superconvergent at most mesh vertices, by local symmetry of the finite element basis with respect to local spatial inversions. As proof of concept that this method is feasible for generating multi-block initial data in three dimensions, the Brill wave is constructed and evolved in time using a high order finite-differencing multi-block approach. Accurate and convergent gravitational wave signal is extracted from the numerical solution.