Seminars and Colloquiums
for the week of May 12, 2019
Wenbo Li, University of Maryland
COMPUTATIONAL and APPLIED MATHEMATICS (CAM) SEMINAR
TITLE: Pointwise Error Estimates for Two-scale method for the Monge-Ampere equation
SPEAKER: Wenbo Li, University of Maryland
TIME: 3:30 PM-4:30 PM
ROOM: Ayres 405
The Monge-Ampere equation is a fully nonlinear second order elliptic PDE that has applications in differential geometry and optimal transportation. In this talk, we will focus on a numerical method called two-scale method introduced by Nochetto, Ntogkas and Zhang for the Monge-Ampere equation, which is a monotone scheme and related to the wide stencil method proposed by Froese and Oberman, and the semi- Lagrangian method proposed by Feng and Jensen. We will show how to derive pointwise error estimates for classical solutions with either Holder or Sobolev regularity by using the discrete comparison principle and the construction of suitable discrete barrier functions. The error estimates for the convex envelope problem, which has connections with the degenerate Monge-Ampere equation, will also be discussed.
(Joint work with Ricardo H. Nochetto)
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Mar. 18, 2019 (Spring break)