Numerical Simulations on Two Nonlinear Biharmonic Evolution Equations

We numerically simulate the following two nonlinear evolution equations with a fourth-order (biharmonic) leading term: and 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.

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