Interior penalty discontinuous Galerkin methods with implicit time‐integration techniques for nonlinear parabolic equations
Interior penalty discontinuous Galerkin methods with implicit time‐integration techniques for nonlinear parabolic equations
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DOI：
10.1002/num.21758
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发表时间：
2013-07
影响因子：
3.9
通讯作者：
Lunji Song;G. Gie;Ming‐Cheng Shiue
中科院分区：
文献类型：
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作者：
Lunji Song;G. Gie;Ming‐Cheng Shiue
证明了求解非线性抛物型方程的三种全离散内罚间断Galerkin方法数值解的存在性和数值稳定性。在适当的正则性条件下，我们给出了全离散对称内罚间断Galerkin格式和隐式θ格式在时间上的l2（H1）和l∞（L2）误差估计，其中包括向后Euler和Crank-Nicolson有限差分逼近.我们的估计对于网格尺寸h是最优的。数值实验验证了理论分析的正确性。© 2012 Wiley Periodicals，Inc. Numer Methods Partial Differential Eq，2013
We prove existence and numerical stability of numerical solutions of three fully discrete interior penalty discontinuous Galerkin methods for solving nonlinear parabolic equations. Under some appropriate regularity conditions, we give the l2(H1) and l∞(L2) error estimates of the fully discrete symmetric interior penalty discontinuous Galerkin–scheme with the implicit θ ‐schemes in time, which include backward Euler and Crank–Nicolson finite difference approximations. Our estimates are optimal with respect to the mesh size h. The theoretical results are confirmed by some numerical experiments. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013