Consistent convergence rate estimates in the grid W 2,0 2 (ω) norm for difference schemes approximating nonlinear elliptic equations with mixed derivatives and solutions from W 2,0 m (Ω), 3 < m ≤ 4

2017 ◽  
Vol 57 (9) ◽  
pp. 1427-1452 ◽  
Author(s):  
F. V. Lubyshev ◽  
M. E. Fairuzov
Keyword(s):  
Convergence Rate ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Difference Schemes ◽  
Nonlinear Elliptic ◽  
Mixed Derivatives

scholarly journals Numerical solution of nonlinear elliptic systems by block monotone iterations

2019 ◽  
Vol 60 ◽  
pp. C79-C94
Author(s):  
Mohamed Saleh Mehdi Al-Sultani ◽  
Igor Boglaev
Keyword(s):  
Iterative Methods ◽  
Elliptic Equations ◽  
Numerical Solutions ◽  
Upper And Lower Solutions ◽  
Elliptic Systems ◽  
Nonlinear Elliptic Equations ◽  
Difference Schemes ◽  
Uniqueness Of Solutions ◽  
Monotone Iterative ◽  
Nonlinear Elliptic

We present numerical methods for solving a coupled system of nonlinear elliptic problems, where reaction functions are quasimonotone nondecreasing. We utilize block monotone iterative methods based on the Jacobi and Gauss--Seidel methods incorporated with the upper and lower solutions method. A convergence analysis and the theorem on uniqueness of solutions are discussed. Numerical experiments are presented. References Boglaev, I., Monotone iterates for solving systems of semilinear elliptic equations and applications, ANZIAM J, Proceedings of the 8th Biennial Engineering Mathematics and Applications Conference, EMAC-2007, 49(2008), C591C608. doi:10.21914/anziamj.v49i0.311 Pao, C. V., Nonlinear parabolic and elliptic equations, Springer-Verlag (1992). doi:10.1007/978-1-4615-3034-3 Pao, C. V., Block monotone iterative methods for numerical solutions of nonlinear elliptic equations, Numer. Math., 72(1995), 239262. doi:10.1007/s002110050168 Samarskii, A., The theory of difference schemes, CRC Press (2001). https://www.crcpress.com/The-Theory-of-Difference-Schemes/Samarskii/p/book/9780824704681 Varga, R. S., Matrix iterative analysis, Springer-Verlag (2000). doi:10.1007/978-3-642-05156-2

A new concept of reduced measure for nonlinear elliptic equations

2004 ◽  
Vol 339 (3) ◽  
pp. 169-174 ◽  
Author(s):  
Haïm Brezis ◽  
Moshe Marcus ◽  
Augusto C. Ponce
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Elliptic
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