Workshop on Foundations of Numerical PDEs

July 7 - July 9, 2005

Universidad de Cantabria in Santander, Spain

On Constraint Preservation in Finite Element Discretizations of Yang-Mills Equations

Snorre Christiansen

CMA / Dept. Math. at University of Oslo

Abstract:   Yang-Mills equations, in their hyperbolic form, are nonlinear wave equations generalizing those of Maxwell. They preserve a nonlinear differential constraint on the initial data, similar to electric charge. Difficulties in preserving such constraints has been perceived to be at the center of numerical instabilities observed in discretizing other evolution equations, such as Einstein's equations of general relativity. We discuss this problem, for finite element discretizations of the Yang-Mills equations, comparing with recent results obtained for the linear (Maxwell) case.