A Nonlinear Wave Equation in Free Capillary Surface Flows
In the study of free capillary flows, one comes across the
nonlinear wave equation
which has the associated conserved energy functional
The following are movies of solutions of this
equation when the domain is disk and the equation
was discretized using a second order in time, centered
finite difference in time and piecewise linear
element in space scheme.
Solutions of the numerical scheme
are guaranteed to be energy nonincreasing (although they
are energy decreasing in practice due to numerical diffusion).
This boundary value problem is well posed for initial data
which lie in the space BV.