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Numerische Mathematik

, Volume 141, Issue 1, pp 253–288 | Cite as

Pointwise rates of convergence for the Oliker–Prussner method for the Monge–Ampère equation

  • Ricardo H. Nochetto
  • Wujun ZhangEmail author
Article

Abstract

We study the Oliker–Prussner method exploiting its geometric nature. We derive discrete stability and continuous dependence estimates in the max-norm by using a discrete Alexandroff estimate and the Brunn–Minkowski inequality. We show that the method is exact for all convex quadratic polynomials provided the underlying set of nodes is translation invariant within the domain; nodes still conform to the domain boundary. . This gives a suitable notion of operator consistency which, combined with stability, leads to pointwise rates of convergence for classical and non-classical solutions of the Monge–Ampère equation.

Mathematics Subject Classification

65N12 65N15 65N30 35J96 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Institute for Physical Science and TechnologyUniversity of MarylandCollege ParkUSA
  2. 2.Department of MathematicsRutgers UniversityNew BrunswickUSA

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