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Title: A convexity enforcing $${C}^{{0}}$$ interior penalty method for the Monge–Ampère equation on convex polygonal domains
Abstract We design and analyze a $$C^0$$ C 0 interior penalty method for the approximation of classical solutions of the Dirichlet boundary value problem of the Monge–Ampère equation on convex polygonal domains. The method is based on an enhanced cubic Lagrange finite element that enables the enforcement of the convexity of the approximate solutions. Numerical results that corroborate the a priori and a posteriori error estimates are presented. It is also observed from numerical experiments that this method can capture certain weak solutions.  more » « less
Award ID(s):
1819161 2110722
NSF-PAR ID:
10260020
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Numerische Mathematik
ISSN:
0029-599X
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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