Some discrete inequalities for central-difference type operators
Hiroki Kojima, Takayasu Matsuo, Daisuke Furihata
Source abstract
Discrete versions of basic inequalities in functional analysis such as the Sobolev inequality play a key role in theoretical analysis of finite difference schemes. They have been shown for some simple difference operators, but are still left open for general operators, even including the standard central difference operators. In this paper, we propose a systematic approach for deriving such inequalities for a certain class of central-difference type operators. We illustrate the results by giving a generic a priori estimate for certain conservative schemes for the nonlinear Schrödinger and Cahn–Hilliard equations.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.