The Numerical approximation of minimal surfaces with free boundaries by finite elements ; Die numerische Approximation von Minimalflächen mit freiem Rand durch Finite Elemente
Titel:
The Numerical approximation of minimal surfaces with free boundaries by finite elements ; Die numerische Approximation von Minimalflächen mit freiem Rand durch Finite Elemente
Anmerkungen:
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Beschreibung:
We develop an efficient method for finding and calculating discrete approximations to following disc-type minimal surfaces with free boundaries: Solution of the Plateau Problem corresponding to a supporting surface S, Solution of the Thread Problem. In both case, the problem is reformulated and the highly nonlinear problem (obtained) is discretized using piecewise linear finite elements. The convergence of the algorithm is proved by means of error estimates for discrete minimal surfaces in the H1-Norm. We also present numerical examples.