The adaptive tensor product wavelet scheme: Sparse matrices and the application to singularly perturbed problems
نویسنده
چکیده
Locally supported biorthogonal wavelets are constructed on the unit interval with respect to which second order constant coefficient differential operators are sparse. As a result, the representation of second order differential operators on the hypercube with respect to the resulting tensor product wavelet coordinates is again sparse. The advantage of tensor product approximation is that it yields (nearly) dimension independent rates. An adaptive tensor product wavelet method is applied to solve various singularly perturbed boundary value problems. The numerical results indicate robustness with respect to the singular perturbations. For a two-dimensional model problem, this will be supported by theoretical results.
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