Higher order derivative estimates for finite-difference schemes

TL;DR

This paper establishes conditions ensuring that finite-difference schemes for certain second order parabolic and elliptic equations can uniformly estimate derivatives of any order, regardless of mesh size.

Contribution

It provides new sufficient conditions for derivative estimates in finite-difference schemes for degenerate second order PDEs.

Findings

Derivative estimates are independent of mesh size.

Applicable to degenerate parabolic and elliptic equations.

Conditions ensure higher order derivative bounds.

Abstract

We give sufficient conditions under which solutions of finite-difference schemes in the space variable for second order possibly degenerate parabolic and elliptic equations admit estimates of spatial derivatives up to any given order independent of the mesh size.