A spline collocation method for multidimensional strongly elliptic pseudodifferential operators of order zero

In the present paper we prove the stability of a nodal spline collocation method for (locally) strongly elliptic zero order pseudodifferential equations inL2 (Ω), where Ω is a bounded Lipschitz domain inℝn. As trial functions we use multi-polynomial splines of odd multi-degree on a rectangular grid. The key of our analysis is the reduction to the case of an operator with frozen symbol by using a local principle due to one of the authors [30]. Moreover, for a right hand sightf ∈H3 (Ω),s>n/2, we obtain an asymptotic error estimate. Finally we extend these results to the case of (locally) strongly elliptic pseudodifferential equations on the torusTn.

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