Abstract:
YangMills 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 YangMills equations, comparing with recent results obtained for the linear (Maxwell) case.
