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We construct a space of vector fields that are normal to differentiablecurves in the plane. Its basis functions are defined via saddle pointvariational problems in reproducing kernel Hilbert spaces (RKHSs). First, westudy the properties of these basis vector fields and show how to approximatethem. Then, we employ this basis to discretise shape Newton methods andinvestigate the impact of this discretisation on convergence rates.

Weakly-normal basis vector fields in RKHS with an application to shape Newton methods