Spline Approximation Methods for the Biharmonic Dirichlet Problem on Non-Smooth Domains

Didenko, Victor D.; Silbermann, Bernd

doi:10.1007/978-3-0348-8199-9_9

Cited by 1 publication

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“…In contrast to [8] then, we consider here these higher order splines and we also study the collocation and qualocation methods. Note that for splines of higher degree the applicability of the corresponding Galerkin method for piece-wise contours was first established in [9]. The authors of [9] also mentioned that for smooth boundaries their result can be simplified.…”

Section: Proposition 1 Let γ Be a Simple Closed Lyapunov Curve And Lmentioning

confidence: 99%

“…Note that for splines of higher degree the applicability of the corresponding Galerkin method for piece-wise contours was first established in [9]. The authors of [9] also mentioned that for smooth boundaries their result can be simplified. However, in the present paper we give a stability proof which is well adjusted to the case of smooth boundaries and does not follow from that in [8].…”

Section: Proposition 1 Let γ Be a Simple Closed Lyapunov Curve And Lmentioning

confidence: 99%

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Approximation methods for the Muskhelishvili equation on smooth curves

Didenko

Venturino

2007

Math. Comp.

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Abstract. We investigate the possibility of applying approximation methods to the famous Muskhelishvili equation on a simple closed smooth curve Γ. Since the corresponding integral operator is not invertible the initial equation has to be corrected in a special way. It is shown that the spline Galerkin, spline collocation and spline qualocation methods for the corrected equation are stable, and the corresponding approximate solutions converge to an exact solution of the Muskhelishvili equation in appropriate norms. Numerical experiments confirm the effectiveness of the proposed methods.

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Section: Proposition 1 Let γ Be a Simple Closed Lyapunov Curve And Lmentioning

confidence: 99%