A Method for the Numerical Solution of Problems Governed by Elliptic Systems in the Cut Plane

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Abstract
A method is derived for the numerical solution of boundary-value problems governed by systems of second order linear elliptic partial differential equations in two independent variables. The boundary of the region in 2under consideration is required to consist of two parts. The first part γ is a straight cut of finite length while the second part C consists of an arbitrary contour surrounding γ The solution to a particular boundary-value problem is expressed in terms of an integral taken around C. This integral may be evaluated numerically. The method should be particularly useful for the solution of crack problems in anisotropic thermostatics and elastostatic

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