Abstract
In the previous chapters, the complex variable boundary element method (CVBEM) is used to develop an approximation function \(\hat{\omega}(\rm z)\) which is analytic in the interior of the domain Ω UΓ ε P, where the boundary Γ is a simply connected contour. The function \(\hat{\omega}(\rm z)\), therefore, exactly satisfies the Laplace equation in Ω and generally approximates the boundary conditions on Γ. Let ω(z) be the solution of the boundary value problem (Laplace equation) on Ω UΓ. Then a relative error function is defined on Ω UΓ by \(\rm e(z)=\omega(z)-\hat{\omega}(z)\). Should e(z) = 0 on Γ, then \(\hat{\omega}(\rm z)=\omega(\rm z)\) on Ω UΓ.
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© 1984 Springer-Verlag Berlin Heidelberg
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Hromadka, T.V. (1984). Reducing CVBEM Approximation Relative Error. In: The Complex Variable Boundary Element Method. Lecture Notes in Engineering, vol 9. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82361-9_5
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DOI: https://doi.org/10.1007/978-3-642-82361-9_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-13743-6
Online ISBN: 978-3-642-82361-9
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