2001•Journal of marine science and technologyOpen access

Natural Doundary Element Method for Elliptic Boundary Value Problems in Domains with Concave Angle

Qikui Du, Dehao Yu

Abstract

In this paper the natural boundary reduction for some elliptic boundary value problems with concave angle domains and its natural boundary element methods are investigated. Natural integral equations and Poisson integral formulae are given. A finite element methods of natural integral equations are discussed in details. The convergence of approximate solutions and their error estimates are obtained. Some numerical experiments are presented to demonstrate the performance of the method and our estimates. As an application, we present the coupling of FEM and natural boundary element.

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Key concepts: Finite element method, Boundary element method, Boundary value problem, Boundary knot method, Mathematics, Mathematical analysis, Convergence (economics), Boundary (topology)