Numerical Simulations on Two Nonlinear Biharmonic Evolution Equations

Abstract

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.

Keywords:

• Nonlinear biharmonic evolution equations
• Ginzburg–Landau type equations
• Bivariate spline method

Acknowledgement

Lai is supported by the National Science Foundation under Grant #DMS-9870178.

Notes

^‡E-mail: [email protected]

^†E-mail: [email protected]

^†E-mail: [email protected]

Additional information

Notes on contributors

Paul Wenston ‡

‡E-mail: [email protected] †E-mail: [email protected]