Enriched Meshfree Method for an Accurate Numerical Solution of the Motz Problem
Author
Source
Advances in Mathematical Physics
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-07-10
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
We present an enriched meshfree solution of the Motz problem.
The Motz problem has been known as a benchmark problem to verify the efficiency of numerical methods in the presence of a jump boundary data singularity at a point, where an abrupt change occurs for the boundary condition.
We propose a singular basis function enrichment technique in the context of partition of unity based meshfree method.
We take the leading terms of the local series expansion at the point singularity and use them as enrichment functions for the local approximation space.
As a result, we obtain highly accurate leading coefficients of the Motz problem that are comparable to the most accurate numerical solution.
The proposed singular enrichment technique is highly effective in the case of the local series expansion of the solution being known.
The enrichment technique that is used in this study can be applied to monotone singularities (of type r α with α < 1 ) as well as oscillating singularities (of type r α sin ( ϵ log r ) ).
It is the first attempt to apply singular meshfree enrichment technique to the Motz problem.
American Psychological Association (APA)
Hong, Won-Tak. 2016. Enriched Meshfree Method for an Accurate Numerical Solution of the Motz Problem. Advances in Mathematical Physics،Vol. 2016, no. 2016, pp.1-12.
https://search.emarefa.net/detail/BIM-1095870
Modern Language Association (MLA)
Hong, Won-Tak. Enriched Meshfree Method for an Accurate Numerical Solution of the Motz Problem. Advances in Mathematical Physics No. 2016 (2016), pp.1-12.
https://search.emarefa.net/detail/BIM-1095870
American Medical Association (AMA)
Hong, Won-Tak. Enriched Meshfree Method for an Accurate Numerical Solution of the Motz Problem. Advances in Mathematical Physics. 2016. Vol. 2016, no. 2016, pp.1-12.
https://search.emarefa.net/detail/BIM-1095870
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1095870