A convexity enforcing $${C}^{{0}}$$ interior penalty method for the Monge–Ampère equation on convex polygonal domains

Autor:	Zhiyu Tan, Li-Yeng Sung, Hongchao Zhang, Susanne C. Brenner
Rok vydání:	2021
Předmět:	Computational Mathematics Applied Mathematics Numerical analysis Regular polygon Applied mathematics A priori and a posteriori Monge–Ampère equation Penalty method Boundary value problem Convexity Finite element method Mathematics
Zdroj:	Numerische Mathematik. 148:497-524
ISSN:	0945-3245 0029-599X
DOI:	10.1007/s00211-021-01210-x
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::ee56fdd5fcb556a147e258851353f0d2 https://doi.org/10.1007/s00211-021-01210-x Zobrazit plný text záznamu Full text from SpringerLink