Abstract
We introduce the notion of δ-viscosity solutions for fully nonlinear uniformly parabolic PDE on bounded domains. We prove that δ-viscosity solutions are uniformly close to the actual viscosity solution, with an explicit error of order δ α. As a consequence we obtain an error estimate for implicit monotone finite difference approximations of uniformly parabolic PDE.
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Turanova, O. Error estimates for approximations of nonlinear uniformly parabolic equations. Nonlinear Differ. Equ. Appl. 22, 345–389 (2015). https://doi.org/10.1007/s00030-014-0286-x
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DOI: https://doi.org/10.1007/s00030-014-0286-x