Error control for the approximation of Allen–Cahn and Cahn–Hilliard equations with a logarithmic potential
Error control for the approximation of Allen–Cahn and Cahn–Hilliard equations with a logarithmic potential
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DOI：
10.1007/s00211-011-0389-9
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发表时间：
2011-11
影响因子：
2.1
通讯作者：
S. Bartels;R. Müller
中科院分区：
文献类型：
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作者：
S. Bartels;R. Müller
导出了对数势Allen-Cahn和Cahn-Hilliard方程有限元逼近误差的一个完全可计算的上界。数值实验表明，对于尖锐的界面极限，这个界是鲁棒的过去的拓扑变化。修改抽象的结果，以获得准最优误差估计在不同的范数最低阶有限元方法进行了讨论，并导致较弱的条件下，条件误差估计的残差。
A fully computable upper bound for the finite element approximation error of Allen–Cahn and Cahn–Hilliard equations with logarithmic potentials is derived. Numerical experiments show that for the sharp interface limit this bound is robust past topological changes. Modifications of the abstract results to derive quasi-optimal error estimates in different norms for lowest order finite element methods are discussed and lead to weaker conditions on the residuals under which the conditional error estimates hold.