二阶椭圆方程的杂化不连续伽辽金法的超收敛性

Minam Moon, Yang Hwan Lim
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引用次数: 0

摘要

摘要。提出了一种新的二阶椭圆方程的可杂化不连续Galerkin方法的投影分析方法。与标准HDG方法相比,该方法具有更高的阶精度和更低的计算成本,并且具有更大的灵活性。与标准HDG方法相比,我们的新方法的显著区别在于,我们的方法使用l2 -投影和合适的稳定参数,这取决于超收敛的网格大小。我们证明了当我们只使用p +1次多项式作为没有后处理的有限元空间时,方程解的误差收敛于p + 2阶。在建立理论基础上,通过数值试验验证了该方法的有效性和准确性。
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SUPERCONVERGENCE OF HYBRIDIZABLE DISCONTINUOUS GALERKIN METHOD FOR SECOND-ORDER ELLIPTIC EQUATIONS
A BSTRACT . We propose a projection-based analysis of a new hybridizable discontinuous Galerkin method for second order elliptic equations. The method is more advantageous than the standard HDG method in a sense that the new method has higher-order accuracy and lower computational cost, and is more flexible. Notable distinctions of our new method, when compared to the standard HDG emthod, are that our method uses L 2 − projection and suitable stabilization parameter depending on a mesh size for superconvergence. We show that the error for the solution of the equation converges with order p + 2 when we only use polynomials of degree p +1 as a finite element space without postprocessing. After establishing the theory, we carry out numerical tests to demonstrate and ensure that the proposed method is effective and accurate in practice.
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