Quadratic Spline Wavelets with Short Support for Fourth-Order Problems
D. Cerná, V. Finěk
Aug 19, 2014
Citations
11
Citations
Journal
Results in Mathematics
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Key Takeaway Key Takeaway: This paper proposes new quadratic spline-wavelet bases with small supports, resulting in uniformly bounded stiffness matrices for fourth-order problems.
Abstract
In the paper, we propose constructions of new quadratic spline-wavelet bases on the interval and the unit square satisfying homogeneous Dirichlet boundary conditions of the second order. The basis functions have small supports and wavelets have one vanishing moment. We show that stiffness matrices arising from discretization of the biharmonic problem using a constructed wavelet basis have uniformly bounded condition numbers and these condition numbers are very small.
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