Numerical Null-Solutions to Iterated Dirac Operator on Bounded Domains

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• 作者：Min Ku ; Uwe Kähler
• 关键词：Discrete Dirac operator ; Almansi ; type decomposition ; Taylor series ; Numerical solutions
• 刊名：Complex Analysis and Operator Theory
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：11
• 期：2
• 页码：307-328
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Operator Theory; Analysis;
• 出版者：Springer International Publishing
• ISSN：1661-8262
• 卷排序：11

文摘

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.