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논문 기본 정보
- 자료유형
- 학술대회자료
- 저자정보
- 발행연도
- 2006.5
- 수록면
- 21 - 26 (6page)
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In a neighborhood of concave edge through the origin in a cylindrical region Q the solution of the Laplace equation with zero Dirichlet data can have a decomposition of the form u=u<SUB>r</SUB>+(c*E)Xr<SUP>π/ω</SUP> sin[(π/ω)(θ-ω₁)] with u<SUB>r</SUB> ∈ H²(Q) and c ∈ H<SUP>1-π/ω</SUP>(?) where ω = ω₂-ω₁ ＞ π is the opening angle, χ is a cutoff function and * is the convolution on the edge. We define the approximations u<SUB>r,h</SUB> and c<SUB>h</SUB> for the regular part ur<SUB> </SUB>and the edge flux intensity function c by applying the inverse Fourier transform to the finite element solution of the Laplace problem with parameter. We derive the error estimate ∥u<SUB>r</SUB>-u<SUB>r,h</SUB>∥<SUB>I,Q</SUB>+∥c-c<SUB>h</SUB>∥<SUB>1-π/ω,R</SUB> ≤ Ch<SUP>1-ε</SUP>∥f∥<SUB>0,Q</SUB>, where ε is an arbitrarily small positive number, which shows the rate of convergence faster than that expected by the regularity of the function c.
목차
ABSTRACT
INTRODUCTION
THE RESULT OF 2-DIMENSIONAL LAPLACE PROBLEM WITH PARAMETER
MAIN RESULT
REFERENCES
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UCI(KEPA) : I410-ECN-0101-2009-410-014678487