Nonlinear elliptic problems with the method of finite volumes
We present a finite volume discretization of the nonlinear elliptic problems. The discretization results in a nonlinear algebraic system of equations. A Newton-Krylov algorithm is also presented for solving the system of nonlinear algebraic equations. Numerically solving nonlinear partial differenti...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | Differential Equations and Nonlinear Mechanics |
| Online Access: | http://dx.doi.org/10.1155/DENM/2006/31797 |
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| _version_ | 1832560955085553664 |
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| author | Sanjay Kumar Khattri |
| author_facet | Sanjay Kumar Khattri |
| author_sort | Sanjay Kumar Khattri |
| collection | DOAJ |
| description | We present a finite volume discretization of the nonlinear
elliptic problems. The discretization results in a nonlinear
algebraic system of equations. A Newton-Krylov algorithm is also
presented for solving the system of nonlinear algebraic
equations. Numerically solving nonlinear partial differential
equations consists of discretizing the nonlinear partial
differential equation and then solving the formed nonlinear
system of equations. We demonstrate the convergence of the
discretization scheme and also the convergence of the Newton
solver through a variety of practical numerical examples. |
| format | Article |
| id | doaj-art-838d4a39e0a749408f8a62cf77e0c3a8 |
| institution | Kabale University |
| issn | 1687-4099 1687-4102 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Differential Equations and Nonlinear Mechanics |
| spelling | doaj-art-838d4a39e0a749408f8a62cf77e0c3a82025-02-03T01:26:15ZengWileyDifferential Equations and Nonlinear Mechanics1687-40991687-41022006-01-01200610.1155/DENM/2006/3179731797Nonlinear elliptic problems with the method of finite volumesSanjay Kumar Khattri0Department of Mathematics, University of Bergen, Bergen 5008, NorwayWe present a finite volume discretization of the nonlinear elliptic problems. The discretization results in a nonlinear algebraic system of equations. A Newton-Krylov algorithm is also presented for solving the system of nonlinear algebraic equations. Numerically solving nonlinear partial differential equations consists of discretizing the nonlinear partial differential equation and then solving the formed nonlinear system of equations. We demonstrate the convergence of the discretization scheme and also the convergence of the Newton solver through a variety of practical numerical examples.http://dx.doi.org/10.1155/DENM/2006/31797 |
| spellingShingle | Sanjay Kumar Khattri Nonlinear elliptic problems with the method of finite volumes Differential Equations and Nonlinear Mechanics |
| title | Nonlinear elliptic problems with the method of finite volumes |
| title_full | Nonlinear elliptic problems with the method of finite volumes |
| title_fullStr | Nonlinear elliptic problems with the method of finite volumes |
| title_full_unstemmed | Nonlinear elliptic problems with the method of finite volumes |
| title_short | Nonlinear elliptic problems with the method of finite volumes |
| title_sort | nonlinear elliptic problems with the method of finite volumes |
| url | http://dx.doi.org/10.1155/DENM/2006/31797 |
| work_keys_str_mv | AT sanjaykumarkhattri nonlinearellipticproblemswiththemethodoffinitevolumes |