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Title: Numerical null-solutions to iterated Dirac operator on bounded domains
Author: Ku, Min
Kähler, Uwe
Keywords: Discrete Dirac operator
Almansi-type decomposition
Taylor series
Numerical solutions
Issue Date: Feb-2017
Publisher: Springer
Abstract: The main purpose of this paper is to study numerical null-solutions to the iterated Dirac operator on bounded domains by using methods of discrete Clifford analysis. First, we study the properties of discrete Euler operators, introduce its inverse operators, and construct a discrete version of the Almansi-type decomposition theorem for the iterated discrete Dirac operator. Then, we give representations of numerical null-solutions to the iterated Dirac operator on a bounded domain in terms of its Taylor series. Finally, in order to illustrate our numerical approach, we present a simple numerical example in form of a discrete approximation of the Stokes’ equation, and show its convergence to the corresponding continuous problem when the lattice constant goes to zero.
Peer review: yes
DOI: 10.1007/s11785-016-0544-5
ISSN: 1661-8254
Appears in Collections:CIDMA - Artigos
CHAG - Artigos

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