TY - JOUR
T1 - Convergence Rate for Difference Schemes for Polyhedral Nonlinear Parabolic Equations
AU - Adam M. Oberman
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 - <p style="text-align: justify;">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.</p>