【摘要】 主要讨论用p-version间断有限元方法(DG)求解一维奇异摄动反应扩散问题。证明了数值解的存在唯一性,并给出了相应的数值算例.数值结果表明,与h-version DG方法相比较,为了达到同样数量级的误差,p-version DG方法的自由度大大下降,并且具有指数收敛性。更多还原

【Abstract】 This paper focuses on the p-version discontinuous Galerkin finite element method(DG) for solving an one-dimensional singularly perturbed reaction-diffusion problem.The uniqueness and existence of the numerical solution is proved and some numerical examples are given.The numerical results show that,compared with the h-version DG method,the freedom of our p-version DG approach decreases greatly when the same error is attained.Furthermore,our approach can converge exponentially.更多还原