Error Analysis for the Finite Element Approximation of Transmission Eigenvalues

Abstract

In this paper we consider the transmission eigenvalue problem corresponding to acoustic scattering by a bounded isotropic inhomogeneous object in two dimensions. This is a non-self-adjoint eigenvalue problem for a quadratic pencil of operators. In particular we are concerned with theoretical error analysis of a finite element method for computing the eigenvalues and corresponding eigenfunctions. Our analysis of convergence makes use of Osborn's perturbation theory for eigenvalues of non-self-adjoint compact operators. Some numerical examples are presented to confirm our theoretical error analysis.

Document Details

Document Type
Pub Defense Publication
Publication Date
Jul 24, 2014
Source ID
10.1515/cmam-2014-0021

Entities

People

  • Fioralba Cakoni
  • Jiguang Sun
  • Peter Monk

Organizations

  • Air Force Office of Scientific Research
  • Michigan Technological University
  • National Science Foundation
  • United States Army Research Laboratory
  • University of Delaware

Tags

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra