LEAST-SQUARES SOLUTIONS OF A GENERAL NUMERICAL METHOD FOR ARBITRARY IRREGULAR GRIDS

This article describes a computational method to calculate solutions of elliptic boundary value problems using arbitrary irregular grids. The main feature of the numerical method is its ability to approximate solutions of di¤erential equations without co-ordinate mapping or metric tensor information. For linear di¤erential equations, the numerical method yields coupled linear systems on local computational cells. Optimal least-squares solutions of coupled linear systems are discussed and applied to the scheme. The numerical method is used to simulate potential ßow for two model problems. The computational results are in very good agreement with analytical solutions