Abstract
In this paper, we study a new Hessian recovery based method for fourth-order differential equations by combining finite element methods (FEMs) and finite difference methods (FDMs). The new C0 finite element method is established under the framework of Petrov–Galerkin methods. Meanwhile, some unsuccessful higher-order methods based on the Hessian recovery operator are also discussed. Finally, we extend our method to solve Cahn-Hilliard equations. Numerical results validate that our proposed C0 method works well for Cahn-Hilliard, with good convergence property and easy implementation.
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