We numerically simulate the following two nonlinear evolution equations with a fourth-order (biharmonic) leading term: (Formula presented.) and (Formula presented.) with an initial value and a Dirichlet boundary conditions. We use a bivariate spline space like finite element method to solve these equations. We discuss the convergence of our numerical scheme and present several numerical experiments under different boundary conditions and different domains in the bivariate setting.
All Science Journal Classification (ASJC) codes
- Environmental Chemistry
- Plant Science