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The Dirac Equation: Numerical and Asymptotic Analysis


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Title: The Dirac Equation: Numerical and Asymptotic Analysis
Authors: Almanasreh, Hasan
E-mail: almanasr@chalmers.se
Issue Date: 28-Nov-2012
University: Göteborgs universitet. Naturvetenskapliga fakulteten
Institution: Department of Mathematical Sciences ; Institutionen för matematiska vetenskaper
Parts of work: Paper I: Stabilized finite element method for the radial Dirac equation. Hasan Almanasreh, Sten Salomonson, and Nils Svanstedt. Submitted

Paper II: $hp$-Cloud approximation of the Dirac eigenvalue problem: The way of stability. Hasan Almanasreh. Manuscript

Paper III: G-convergence of Dirac operators. Hasan Almanasreh and Nils Svanstedt. Published in Journal of Function Spaces and Applications
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Paper IV: On G-convergence of positive self-adjoint operators. Hasan Almanasreh. Submitted

Paper V: Strong convergence of wave operators for a family of Dirac operators. Hasan Almanasreh. Submitted

paper VI: Existence and asymptotics of wave operators for self-adjoint operators. Hasan Almanasreh. Manuscript
Date of Defence: 2012-12-20
Disputation: December 20, 2012, at 10.15 in room Pascal, Deparment of Mathematical Sciences, Chalmers Tvärgata 3, Gothenburg.
Degree: Doctor of Philosophy
Publication type: Doctoral thesis
Keywords: Dirac operator, eigenvalue problem, finite element method, spurious eigenvalues, Petrov-Galerkin, cubic Hermite basis functions, stability parameter, meshfree method, $hp$-cloud, intrinsic enrichment, G-convergence, $\Gamma$-convergence, scattering theory, identification, wave operator, stationary approach
Abstract: The thesis consists of three parts, although each part belongs to a specific subject area in mathematics, they are considered as subfields of the perturbation theory. The main objective of the presented work is the study of the Dirac operator; the first part concerns the treatment of the spurious eigenvalues in the computation of the discrete spectrum. The second part considers G-convergence theory for positive definite parts of a family of Dirac operators and general positive definite self-adjo... more
ISBN: 978-91-628-8593-9
URI: http://hdl.handle.net/2077/31247
Appears in Collections:Doctoral Theses from University of Gothenburg / Doktorsavhandlingar från Göteborgs universitet
Doctoral Theses / Doktorsavhandlingar Institutionen för matematiska vetenskaper

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