Volume 28, Issue 4
Convergence Rate for Difference Schemes for Polyhedral Nonlinear Parabolic Equations

J. Comp. Math., 28 (2010), pp. 474-488.

Published online: 2010-08

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• Abstract

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.

• Keywords

Error estimates, Convergence rate, Viscosity solutions, Finite difference schemes

65M06, 65M12.

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@Article{JCM-28-474, author = {}, title = {Convergence Rate for Difference Schemes for Polyhedral Nonlinear Parabolic Equations}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {4}, pages = {474--488}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1003-m0013}, url = {http://global-sci.org/intro/article_detail/jcm/8533.html} }
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.

Adam M. Oberman. (2019). Convergence Rate for Difference Schemes for Polyhedral Nonlinear Parabolic Equations. Journal of Computational Mathematics. 28 (4). 474-488. doi:10.4208/jcm.1003-m0013
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