A Numerical Method for Solving 3D Elasticity Equations with Sharp-Edged Interfaces
Joint Authors
Wang, Liqun
Hou, Songming
Shi, Liwei
Source
International Journal of Partial Differential Equations
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-07-21
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
Interface problems occur frequently when two or more materials meet.
Solving elasticity equations with sharp-edged interfaces in three dimensions is a very complicated and challenging problem for most existing methods.
There are several difficulties: the coupled elliptic system, the matrix coefficients, the sharp-edged interface, and three dimensions.
An accurate and efficient method is desired.
In this paper, an efficient nontraditional finite element method with nonbody-fitting grids is proposed to solve elasticity equations with sharp-edged interfaces in three dimensions.
The main idea is to choose the test function basis to be the standard finite element basis independent of the interface and to choose the solution basis to be piecewise linear satisfying the jump conditions across the interface.
The resulting linear system of equations is shown to be positive definite under certain assumptions.
Numerical experiments show that this method is second order accurate in the L∞ norm for piecewise smooth solutions.
More than 1.5th order accuracy is observed for solution with singularity (second derivative blows up).
American Psychological Association (APA)
Wang, Liqun& Hou, Songming& Shi, Liwei. 2013. A Numerical Method for Solving 3D Elasticity Equations with Sharp-Edged Interfaces. International Journal of Partial Differential Equations،Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-474666
Modern Language Association (MLA)
Wang, Liqun…[et al.]. A Numerical Method for Solving 3D Elasticity Equations with Sharp-Edged Interfaces. International Journal of Partial Differential Equations No. 2013 (2013), pp.1-13.
https://search.emarefa.net/detail/BIM-474666
American Medical Association (AMA)
Wang, Liqun& Hou, Songming& Shi, Liwei. A Numerical Method for Solving 3D Elasticity Equations with Sharp-Edged Interfaces. International Journal of Partial Differential Equations. 2013. Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-474666
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-474666