This article presents the development and examination of a hybrid high-order (HHO) approach tailored for solving a semilinear Sobolev equation on polygonal meshes. The HHO method offers distinct advantages over traditional approaches, demonstrating its capability to achieve higher-order accuracy while reducing the number of unknown coefficients. We establish error approximations for the semi-discrete formulation employing HHO discretization. Using this method we find optimally convergence of orders \(\mathcal{O} \big(\tau^2+h^{k+1}\big)\) in the energy-type norm and \(\mathcal{O} \big(\tau^2+h^{k+2}\big)\) in the \({L}^2\) norm.

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