TY - JOUR
T1 - Fast spectral Galerkin method for logarithmic singular equations on a segment
AU - Jerez-Hanckes, Carlos
AU - Nicaise, Serge
AU - Urzúa-Torres, Carolina
N1 - Funding Information:
Proof. Since ψ∗ = ±∑(1 − η±)p±, we easily show that it belongs to Wm by using Leibniz rule and Faa di Bruno’s formula. The conclusion follows from the definition of p±. □ Acknowledgments. The authors would like to thank Prof. Christoph Schwab and JoséPinto for their insightful remarks over a draft of the current manuscript. This work was supported by Fondecyt Regular 1171491, Conicyt Anillo ACT1417 and CORFO Engineering 2030 program through Grant OPEN-UC 201603.
Publisher Copyright:
© 2019 Global Science Press. All rights reserved.
PY - 2019
Y1 - 2019
N2 - We present a fast Galerkin spectral method to solve logarithmic singular equations on segments. The proposed method uses weighted first-kind Chebyshev polynomials. Convergence rates of several orders are obtained for fractional Sobolev spaces He −1/2 (or H00 −1/2). Main tools are the approximation properties of the discretization basis, the construction of a suitable Hilbert scale for weighted L2-spaces and local regularity estimates. Numerical experiments are provided to validate our claims.
AB - We present a fast Galerkin spectral method to solve logarithmic singular equations on segments. The proposed method uses weighted first-kind Chebyshev polynomials. Convergence rates of several orders are obtained for fractional Sobolev spaces He −1/2 (or H00 −1/2). Main tools are the approximation properties of the discretization basis, the construction of a suitable Hilbert scale for weighted L2-spaces and local regularity estimates. Numerical experiments are provided to validate our claims.
KW - Boundary integral operators
KW - Screen problems
KW - Spectral methods
UR - http://www.scopus.com/inward/record.url?scp=85072517162&partnerID=8YFLogxK
U2 - 10.4208/JCM.1612-M2016-0495
DO - 10.4208/JCM.1612-M2016-0495
M3 - Article
AN - SCOPUS:85072517162
SN - 0254-9409
VL - 36
SP - 128
EP - 158
JO - Journal of Computational Mathematics
JF - Journal of Computational Mathematics
IS - 1
ER -