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Stability of a spline collocation method for strongly elliptic multidimensional singular integral equations

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We consider a spline collocation method for strongly elliptic zero order pseudodifferential equationsp gw Au=f on a cube ω=(0, 1)m. Utilizing multilinear spline functions which are zero at the boundary σω we collocate at the meshpoints inside ω. For classical strongly elliptic translation invariant pseudodifferential operators, we verify the stability of the considered collocation method inL 2(ω). Afterwards, form≦2 and a right hand sidef∈H 8(ω),s>m/2, we prove an asymptotic convergence estimate.

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  1. Fachbereich Mathematik, Technische Hochschule Darmstadt, W-6100, Darmstadt, Germany

    R. Schneider

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  1. R. Schneider
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The author has been supported by a grant of Deutsche Forschungsgemeinschaft under grant number Ko 634/32-1

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Schneider, R. Stability of a spline collocation method for strongly elliptic multidimensional singular integral equations. Numer. Math. 58, 855–873 (1990). https://doi.org/10.1007/BF01385658

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