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A convergent iterated quasi-interpolation for periodic domain and its applications to surface PDEs. (English) Zbl 07593940

A tensor-product quasi-interpolation scheme based on the periodic multiquadric trigonometric kernel is proposed for approximating derivatives and solving time-dependent PDEs on a parametrized surface. Theoretical convergence results are presented, along with several examples of numerical simulations for reaction-diffusion equations on the torus.

MSC:

41A05 Interpolation in approximation theory
41A25 Rate of convergence, degree of approximation
41A30 Approximation by other special function classes
41A63 Multidimensional problems
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