On a Simple Method to Compute Polygonal Minimal Surfaces
نویسنده
چکیده
Given a closed polygonal contour with N+3 vertices in IR q (q 2) there is a one to one correspondence between the zeros of r and minimal surfaces spanned by ?, where () := inf v2X() D(v) (2 T IR N) denotes Shiiman's function for the polygon ? and D denotes Dirichlet's Integral. We derive an explicit expression for r h , where h () := inf v2X h () D(v) with suitable nite element spaces X h (). Furthermore we assure that each zero of r h is also approximately a zero of r and vice-versa. Using quasi-newton-methods and variants of Newton's Method, several examples of minimal surfaces are computed.
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