Abstract In this paper, we study and analyse the hybridized discontinuous Galerkin method for the reaction-diffusion problem. We present a mixed formulation based on some operators with discontinuous piecewise polynomials in a shape regular partition. We prove the well posedness of the mixed scheme and establish some error estimates with optimal order of convergence. Finally, we give some numerical simulations to confirm the convergence results and to validate the mixed formulation.

中文翻译：

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反应扩散方程的hdg法分析

摘要 在本文中，我们研究和分析了反应扩散问题的混合不连续伽辽金方法。我们提出了一种基于一些算子的混合公式，这些算子在形状规则分区中具有不连续的分段多项式。我们证明了混合方案的适定性，并建立了一些具有最优收敛顺序的误差估计。最后，我们给出了一些数值模拟来确认收敛结果并验证混合公式。