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A gradient flow scheme for nonlinear fourth order equations (CROSBI ID 167268)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Duering, Bertram ; Matthes, Daniel ; Milišić, Josipa Pina A gradient flow scheme for nonlinear fourth order equations // Discrete and continuous dynamical systems-series b, 14 (2010), 3; 935-959

Podaci o odgovornosti

Duering, Bertram ; Matthes, Daniel ; Milišić, Josipa Pina

engleski

A gradient flow scheme for nonlinear fourth order equations

We propose a method for numerical integration of Wasserstein gradient flows based on the classical minimizing movement scheme. In each time step, the discrete approximation is obtained as the solution of a constrained quadratic minimization problem on a finite-dimensional function space. Our method is applied to the nonlinear fourth-order Derrida-Lebowitz-Speer-Spohn equation, which arises in quantum semiconductor theory. We prove well-posedness of the scheme and derive a priori estimates on the discrete solution. Furthermore, we present numerical results which indicate second-order convergence and unconditional stability of our scheme. Finally, we compare these results to those obtained from different semi- and fully implicit finite difference discretizations.

wasserstein gradient flow; higher-order diffusion equation; numerical solution

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Podaci o izdanju

14 (3)

2010.

935-959

objavljeno

1531-3492

Povezanost rada

Matematika

Indeksiranost