New C⁰ Interior Penalty Method for Monge-Ampère Equations
Abstract
Monge-Ampère equation is a prototype second-order fully nonlinear partial differential equation. Based on the vanishing moment representation, we approximate the Monge-Ampère equation by a fourth order semi-linear equation with some additional boundary conditions. We propose a new idea to design and analyze the C⁰ interior penalty method to approximate the resulting fourth-order semi-linear equation. The new method is inspired by the discrete Miranda-Talenti estimate. We use the discrete Miranda-Talenti estimates to ensure the well-posedness of the numerical scheme and derive the error estimates.
Fields of Study & Subjects
Geometry and complex manifolds
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Communications in Computational Physics
- Publisher
- Global Science Press
- Volume
- 40
- Issue
- 5
- Pages
- 1447–1472
- Publication date
- 18 June 2026
- Language
- EN