The virtual element method is an extension of the finite element method on polygonal meshes. The virtual element basis functions are generally unknown inside an element and suitable projections of the basis functions onto polynomial spaces are used to construct the elemental stiffness and mass matrices. We present a gradient recovery method based on an oblique projection, where the gradient of the L2-polynomial projection of a solution is projected onto a virtual element space. This results in a computationally efficient numerical method. We present numerical results computing the gradients on different polygonal meshes to demonstrate the flexibility of the method.
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A $C^1$ Virtual Element Method for the Cahn--Hilliard Equation with Polygonal Meshes
