# Convergence Rate of a Stable, Monotone and Consistent Scheme for the Monge-Ampère Equation

## Abstract

**:**

## 1. Introduction

## 2. Notations and Preliminaries

#### 2.1. Consistency

## 3. Rate of Convergence

**Lemma 3.1.**There exists a positive constant $a<1$ such that for all ${v}^{h},{w}^{h}\in \mathcal{M}\left({\mathsf{\Omega}}^{h}\right)$, we have

**Theorem 3.2.**For a solution ${u}^{h}$ of Equation (9) and for $u\in {C}^{4}\left(\overline{\mathsf{\Omega}}\right)$ we have

**Remark 3.3.**The approach in the proof of the previous theorem also gives stability of a solution of Equation (9) in the general case, when f is uniformly bounded. We have

## Acknowledgments

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**MDPI and ACS Style**

Awanou, G.
Convergence Rate of a Stable, Monotone and Consistent Scheme for the Monge-Ampère Equation. *Symmetry* **2016**, *8*, 18.
https://doi.org/10.3390/sym8040018

**AMA Style**

Awanou G.
Convergence Rate of a Stable, Monotone and Consistent Scheme for the Monge-Ampère Equation. *Symmetry*. 2016; 8(4):18.
https://doi.org/10.3390/sym8040018

**Chicago/Turabian Style**

Awanou, Gerard.
2016. "Convergence Rate of a Stable, Monotone and Consistent Scheme for the Monge-Ampère Equation" *Symmetry* 8, no. 4: 18.
https://doi.org/10.3390/sym8040018