Abstract
In this article, we design and analyze a hybrid high-order method for a semilinear Sobolev model on polygonal meshes. The method offers distinct advantages over traditional approaches, demonstrating its capability to achieve higher-order accuracy while reducing the number of unknown coefficients. We derive error estimates for the semi-discrete formulation of the method. Subsequently, these convergence rates are employed in full discretization with the Crank–Nicolson scheme. The method is demonstrated to converge optimally with orders of O(τ2+hk+1) in the energy-type norm and O(τ2+hk+2) in the L2 norm. The reported method is supported by a series of computational tests encompassing linear, semilinear and Allen–Cahn models.
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