Numerical error analysis for nonsymmetric interior penalty discontinuous Galerkin method of Cahn–Hilliard equation
Numerical error analysis for nonsymmetric interior penalty discontinuous Galerkin method of Cahn–Hilliard equation
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DOI：
10.1002/num.22362
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发表时间：
2019-02
影响因子：
3.9
通讯作者：
Chen Liu;F. Frank;B. Rivière
中科院分区：
文献类型：
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作者：
Chen Liu;F. Frank;B. Rivière
在本文中，我们对求解 Cahn-Hilliard 方程的非对称内罚间断伽辽金方法进行了理论分析。我们证明了离散系统的无条件唯一可解性，并推导出具有广义化学能量密度的稳定性界限。该方法的收敛性是通过最优先验误差估计来获得的。我们的分析对于不连续伽辽金公式的对称和非对称版本都有效。
In this paper, we derive a theoretical analysis of nonsymmetric interior penalty discontinuous Galerkin methods for solving the Cahn–Hilliard equation. We prove unconditional unique solvability of the discrete system and derive stability bounds with a generalized chemical energy density. Convergence of the method is obtained by optimal a priori error estimates. Our analysis is valid for both symmetric and nonsymmetric versions of the discontinuous Galerkin formulation.