How to obtain an accurate gradient for interface problems?

JOURNAL OF COMPUTATIONAL PHYSICS

卷:405

Article

Tong, Fenghua¹  Wang, Weilong¹  Feng, Xinlong¹  Zhao, Jianping¹  Li, Zhilin^2,3 

[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China

[2] North Carolina State Univ, CRSC, Raleigh, NC 27695 USA

[3] North Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

关键词: Accuracy of derivatives;    Elliptic interface problems;    Discontinuous coefficient;    Discrete Green functions;    IIM;   

DOI  :  10.1016/j.jcp.2019.109070

来源: Elsevier

【 摘 要 】

It is well-known that the Immersed Interface Method (IIM) is second order accurate for interface problems. But the accuracy of the first order derivatives, or gradients for short, is not so clear and is often assumed to be first order accurate. In this paper, new strategies based on IIM are proposed for elliptic interface problems to compute the gradient at grid points both regular and irregular, and at the interface from each side of the interface. Second order in 1D, or nearly second order (except a factor of vertical bar logh vertical bar) convergence in 2D of the computed gradient is obtained with almost no extra cost, and has been explained in intuition and verified by non-trivial numerical tests. Numerical examples in one, two dimensions, radial and axis-symmetric cases in polar and spherical coordinates are presented to validate the numerical methods and analysis. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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