Spectral element method for three dimensional elliptic problems with smooth interfaces

被引：8

作者：

Khan, Arbaz ^{[1
]}

Husain, Akhlaq ^{[2
]}

Mohapatra, Subhashree ^{[3
]}

Upadhyay, Chandra Shekhar ^{[4
]}

机构：

[1] Heidelberg Univ, Interdisziplinares Zentrum Wissensch Rechnen IWR, D-69120 Heidelberg, Germany

[2] BML Munjal Univ, Sch Engn & Technol, Gurgaon 122413, India

[3] Univ Florida, Dept Math, Gainesville, FL 32601 USA

[4] Indian Inst Technol, Dept Aerosp Engn, Kanpur 208016, Uttar Pradesh, India

来源：

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2017年 / 315卷

关键词：

Least-squares methods; Non-conforming spectral element method; Linear elliptic PDE in three dimensions; Interfaces; Preconditioner; Exponential accuracy; BOUNDARY-VALUE-PROBLEMS; NONSMOOTH DOMAINS; DISCONTINUOUS COEFFICIENTS; SHARP EDGES; MATCHED INTERFACE; MIB METHOD; P-VERSION; PART-I; DIFFERENTIAL-EQUATIONS; MAXWELLS EQUATIONS;

D O I：

10.1016/j.cma.2016.11.003

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper we propose a least-squares spectral element method for three dimensional elliptic interface problems. The differentiability estimates and the main stability theorem, using non-conforming spectral element functions, are proven. The proposed method is free from any kind of first order reformulation. A suitable preconditioner is constructed with help of the regularity estimate and proposed stability estimates which is used to control the condition number. We show that these preconditioners are spectrally equivalent to the quadratic forms by which we approximate them. We obtain the error estimates which show the exponential accuracy of the method. Numerical results are obtained for both straight and curved interfaces to show the efficiency of the proposed method. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：522 / 549

页数：28

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