Tangent-point energies as Gamma-limit of discrete tangent-point energies on biarc curves
Anna Lagemann (RWTH Aachen University)
Abstract: Using interpolation with biarc curves we prove $\Gamma$-convergence of discretized tangent-point energies to the continuous tangent-point energies in the $C^1$-topology. As a consequence, discrete almost minimizing biarc curves converge to minimizers of the continuous tangent-point energies. In addition, taking point-tangent data from a given $C^{1,1}$-curve $\gamma$, we establish convergence of the discrete energies evaluated on biarc curves interpolating these data, to the continuous tangent-point energy of $\gamma$, together with an explicit convergence rate. This is joint work with Heiko von der Mosel.
mathematical physicsanalysis of PDEsclassical analysis and ODEsdifferential geometryfunctional analysismetric geometrynumerical analysisoptimization and control
Audience: researchers in the topic
( paper )
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