OPTIMAL CONSTANTS IN NONTRAPPING RESOLVENT ESTIMATES AND APPLICATIONS IN NUMERICAL ANALYSIS

Jeffrey Galkowski, Euan A. Spence, Jared Wunsch

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

We study the resolvent for nontrapping obstacles on manifolds with Euclidean ends. It is well known that for such manifolds the outgoing resolvent satisfies (Formula Presented), but the constant C has been little studied. We show that, for high frequencies, the constant is bounded above by (Formula Presented) times the length of the longest generalized bicharacteristic of (Formula Presented) remaining in the support of x We show that this estimate is optimal in the case of manifolds without boundary. We then explore the implications of this result for the numerical analysis of the Helmholtz equation.

Original languageEnglish (US)
Pages (from-to)157-202
Number of pages46
JournalPure and Applied Analysis
Volume2
Issue number1
DOIs
StatePublished - 2020

Keywords

  • finite element method
  • Helmholtz equation
  • nontrapping
  • resolvent
  • variable wave speed

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics

Fingerprint

Dive into the research topics of 'OPTIMAL CONSTANTS IN NONTRAPPING RESOLVENT ESTIMATES AND APPLICATIONS IN NUMERICAL ANALYSIS'. Together they form a unique fingerprint.

Cite this