A rate of convergence for monotone finite difference approximations to fully nonlinear, uniformly elliptic PDEs
By Luis Caffarelli, Panagiotis E. Souganidis. 2008
115 citations recorded by the source corpus.
Subfields: Applied Mathematics, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/81252b251298a1d9d964f224d9a92b3a4a62ee67
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- S. Armstrong
- Charles K. Smart
- Panagiotis E. Souganidis
- Espen Robstad Jakobsen
- Kenneth Hvistendahl Karlsen
- Björn Engquist
- Sylvia Serfaty
- Luis Silvestre
In Modeling and Simulation
- S. Armstrong
- Panagiotis E. Souganidis
- Espen Robstad Jakobsen
- Björn Engquist
- Kenneth Hvistendahl Karlsen
- Charles K. Smart
- Luis Caffarelli
- Luis Silvestre
Citations in the corpus
- Rates of convergence for the homogenization of fully nonlinear uniformly elliptic pde in random media (2010, methodology): “This was done for the first time for fully nonlinear equations by the authors in [ 4 ] to obtain error estimates for monotone approximations to uniformly elliptic second order pde.”
- Partial regularity of solutions of fully nonlinear, uniformly elliptic equations (2011, methodology): “[4] L. A. Caffarelli and P. E. Souganidis.”
- A deterministic‐control‐based approach to fully nonlinear parabolic and elliptic equations (2010, background): “Recently Caffarelli and Souganidis have shown how refined consistency results can sometimes be used to prove convergence with a rate, though the viscosity solution may not be differentiable [12, 13].”
- Asymptotic and numerical homogenization (2008, methodology): “The rate of convergence for the periodic homogenization ofF ( D2uε, x ε ) = f in U, uε = g on ∂U, (6.2) was obtained recently by Caffarelli and Souganidis (2008).”
- Viscosity Solutions for a System of Integro-PDEs and Connections to Optimal Switching and Control of Jump-Diffusion Processes (2010, background): “We also mention [16, 18] as important recent contributions in this area.”