TY - JOUR T1 - Convergence Rate for Difference Schemes for Polyhedral Nonlinear Parabolic Equations JO - Journal of Computational Mathematics VL - 4 SP - 474 EP - 488 PY - 2010 DA - 2010/08 SN - 28 DO - http://doi.org/10.4208/jcm.1003-m0013 UR - https://global-sci.org/intro/article_detail/jcm/8533.html KW - Error estimates, Convergence rate, Viscosity solutions, Finite difference schemes AB -

We build finite difference schemes for a class of fully nonlinear parabolic equations. The schemes are polyhedral and grid aligned. While this is a restrictive class of schemes, a wide class of equations are well approximated by equations from this class. For regular $(C^{2,\alpha})$ solutions of uniformly parabolic equations, we also establish of convergence rate of $\mathcal{O}(\alpha)$. A case study along with supporting numerical results is included.