Wavelet Collocation on the Triangle

S. Bertoluzza

We describe two ways of constructing a restriction to the triangle of wavelet interpolating spaces of order N. For both constructions it is possible to prove that polynomials are locally contained in the scale spaces. This implies good approximation properties, and, for the first construction also a result of characterization of regularity via the related multiscale decomposition. Such bases are applied to some elliptic equations by means of an adaptive collocation technique. The results of the first tests show that the construction of the basis on the triangle proposed is indeed a good generalization of wavelets bases on such a domain.

Pubbl. I.A.N. n. 968 (1995)

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