# Monotone discretization of elliptic problems with mixed derivatives on anisotropic meshes: a counterexample

## TL;DR

This paper provides a counterexample demonstrating the challenges of monotone discretization for elliptic problems with mixed derivatives on anisotropic meshes, highlighting limitations in existing numerical methods.

## Contribution

It introduces a specific counterexample that shows the failure of monotone discretization schemes in certain anisotropic mesh configurations for elliptic PDEs with mixed derivatives.

## Key findings

- Counterexample shows monotone discretization failure on anisotropic meshes
- Highlights limitations of current numerical schemes for mixed derivative problems
- Provides insights for developing more robust discretization methods

## Abstract

We present a counterexample concerning the monotone discretization of elliptic problems with mixed derivatives on anisotropic meshes.