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Numerical Solutions to Nonsmooth Dirichlet Problems Based on Lumped Mass Finite Element Discretization
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-01-19
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We apply a lumped mass finite element to approximate Dirichlet problems for nonsmooth elliptic equations.
It is proved that the lumped mass FEM approximation error in energy norm is the same as that of standard piecewise linear finite element approximation.
Under the quasi-uniform mesh condition and the maximum angle condition, we show that the operator in the finite element problem is diagonally isotone and off-diagonally antitone.
Therefore, some monotone convergent algorithms can be used.
As an example, we prove that the nonsmooth Newton-like algorithm is convergent monotonically if Gauss-Seidel iteration is used to solve the Newton's equations iteratively.
Some numerical experiments are presented.
American Psychological Association (APA)
Yu, Haixiong& Zeng, Jinping. 2014. Numerical Solutions to Nonsmooth Dirichlet Problems Based on Lumped Mass Finite Element Discretization. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-1014216
Modern Language Association (MLA)
Yu, Haixiong& Zeng, Jinping. Numerical Solutions to Nonsmooth Dirichlet Problems Based on Lumped Mass Finite Element Discretization. Abstract and Applied Analysis No. 2014 (2014), pp.1-9.
https://search.emarefa.net/detail/BIM-1014216
American Medical Association (AMA)
Yu, Haixiong& Zeng, Jinping. Numerical Solutions to Nonsmooth Dirichlet Problems Based on Lumped Mass Finite Element Discretization. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-1014216
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1014216