Affine Discontinuous Galerkin Method Approximation of Second-Order Linear Elliptic Equations in Divergence Form with Right-Hand Side in L1
Joint Authors
Lidouh, Abdeluaab
Messaoudi, Rachid
Source
International Journal of Differential Equations
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-07-02
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
We consider the standard affine discontinuous Galerkin method approximation of the second-order linear elliptic equation in divergence form with coefficients in L∞Ω and the right-hand side belongs to L1Ω; we extend the results where the case of linear finite elements approximation is considered.
We prove that the unique solution of the discrete problem converges in W01,qΩ for every q with 1≤q Statements and proofs remain valid in our case, which permits obtaining a weaker result when the right-hand side is a bounded Radon measure and, when the coefficients are smooth, an error estimate in W01,qΩ when the right-hand side f belongs to LrΩ verifying Tkf∈H1Ω for every k>0, for some r>1.
American Psychological Association (APA)
Lidouh, Abdeluaab& Messaoudi, Rachid. 2018. Affine Discontinuous Galerkin Method Approximation of Second-Order Linear Elliptic Equations in Divergence Form with Right-Hand Side in L1. International Journal of Differential Equations،Vol. 2018, no. 2018, pp.1-15.
https://search.emarefa.net/detail/BIM-1170766
Modern Language Association (MLA)
Lidouh, Abdeluaab& Messaoudi, Rachid. Affine Discontinuous Galerkin Method Approximation of Second-Order Linear Elliptic Equations in Divergence Form with Right-Hand Side in L1. International Journal of Differential Equations No. 2018 (2018), pp.1-15.
https://search.emarefa.net/detail/BIM-1170766
American Medical Association (AMA)
Lidouh, Abdeluaab& Messaoudi, Rachid. Affine Discontinuous Galerkin Method Approximation of Second-Order Linear Elliptic Equations in Divergence Form with Right-Hand Side in L1. International Journal of Differential Equations. 2018. Vol. 2018, no. 2018, pp.1-15.
https://search.emarefa.net/detail/BIM-1170766
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1170766