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Description: |
The stability of discrete projections on multiple knot periodic splines on uniform
meshes is studied. Results include their approximation power in Sobolev spaces, commutator and superapproximation properties. As an application the convergence of the qualocation method for elliptic periodic pseudodifferential
operators with multiple knot splines as test and trial spaces is analyzed.
[1] R.D. Grigorieff and I. Sloan: Discrete orthogonal projections on multiple knot periodic splines. J. Approx. Th. 137, 201-225 (2005).
[2] R.D. Grigorieff and I. Sloan: Qualocation for boundary integral equations using splines with multiple knots. J. Integral Equations Appl. 18, 117-140 (2006).
[3] R. D. Grigorieff: Superapproximation for projections on spline spaces. Numer. Math. 99, 657-668 (2005).
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