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Title: narrow-stencil framework for convergent numerical approximations of fully nonlinear second order PDEs
This article develops a unified general framework for designing convergent finite difference and discontinuous Galerkin methods for approximating viscosity and regular solutions of fully nonlinear second order PDEs. Unlike the well-known monotone (finite difference) framework, the proposed new framework allows for the use of narrow stencils and unstructured grids which makes it possible to construct high order methods. The general framework is based on the concepts of consistency and g-monotonicity which are both defined in terms of various numerical derivative operators. Specific methods that satisfy the framework are constructed using numerical moments. Admissibility, stability, and convergence properties are proved,and numerical experiments are provided along with some computer implementation details. For more information see https://ejde.math.txstate.edu/conf-proc/26/f1/abstr.html  more » « less
Award ID(s):
2111059
PAR ID:
10423837
Author(s) / Creator(s):
; ;
Publisher / Repository:
Department of Mathematics, Texas State University
Date Published:
Journal Name:
Electronic Journal of Differential Equations
Issue:
Conference 26
ISSN:
1072-6691
Page Range / eLocation ID:
59 to 95
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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