A gradient flow scheme for nonlinear fourth order equations (Q612886)

The authors propose a fully discrete variant of the minimizing movement scheme for the numerical solution of the nonlinear fourth order Derrida-Lebowitz-Speer-Spohn equation. In each time step, a discrete approximation is obtained as the solution of a constrained quadratic minimization problem on a finite dimensional function space. The well-posedness of the scheme is proved and some a priori estimates are obtained. The results are compared to those obtained from different semi and fully implicit finite difference discretizations.