Convergence of an implicit, constraint preserving finite element discretization of p-harmonic heat flow into spheres

We propose an implicit discretization of the p-harmonic map heat flow into the sphere S2 that enjoys a discrete energy inequality and converges under only a mild mesh constraint to a weak solution. A fully practical iterative scheme that approximates the solution of the nonlinear system of equations in each time step is proposed and analyzed. Computational studies to motivate possible finite-time blow-up behavior of solutions for p ≠ 2 are included.