본문 바로가기
KERD
논문KCI 등재

Preconditioning Cubic Spline Collocation Methods for a Cou- pled Elliptic Equation

김상동|신병춘
경북대학교 자연과학대학 수학과|2010.09|Kyungpook Mathematical Journal|제50권 제3호|pp. 419-431

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

Coupled elliptic equationsCubic spline collocation methodsFinite element preconditioner
주제분류수학

초록

A low-order nite element preconditioner is analyzed for a cubic spline collocation method which is used for discretizations of coupled elliptic problems derived from an optimal control problrm subject to an elliptic equation. Some numerical evidences area also provided.

Abstract

A low-order nite element preconditioner is analyzed for a cubic spline collocation method which is used for discretizations of coupled elliptic problems derived from an optimal control problrm subject to an elliptic equation. Some numerical evidences area also provided.

참고문헌 (15)

  1. P. Bochev, "Least-squares finite element methods for optimality systems arising in optimization and control problems", SIAM J. Numer. Anal., 43, pp.2517~2543 (2006)
  2. Y. Chen, "A Legendre-Galerkin spectral method for optimal control problems governed by elliptic equations", SIAM J. Numer. Anal., 46, pp.2254~2275 (2008)
  3. J. Douglas, "Collocation methods for parabolic equations in a single space variable, Lecture Notee in Mathematics 385" (2002), Springer-Verlag Press
  4. S. C. Eisenstat, "Variational iterative methods for nonsymmetric systems of linear equations", SIAM J. Numer. Anal., 20, pp.345~357 (1983)
  5. A. Greenbaum, "Iterative methods for solving linear systems" (1997), SIAM
  6. M. Gunzburger, "Perspectives in Flow Control and Optimization" (2002), SIAM
  7. R. A. Horn, "Topics in Matrix Analysis" (1994), Cambridge University Press
  8. S. D. Kim, "Piecewise bilinear preconditioning of high-order finite element methods", ETNA, 26, pp.228~242 (2007)
  9. S. Kim, "Preconditioning on high-order element methods using Chebyshev-Gauss-Lobatto notes", Applied Numerical Mathematics, 59, pp.316~333 (2009)
  10. S. D. Kim, "Exponential decay of C1-cubic splines vanishiing at two symmetric points in each knot interval", Numer. Math., 76, pp.470~488 (1997)
  11. S. D. Kim, "Preconditioning Chebyshev spectral collocation method for elliptic partial differential equations", SIAM J. Numer. Anal., 33, pp.2375~2400 (1996)
  12. S. D. Kim, "Preconditioning cubic spline collocation discretizations of elliptic equatio", Numer. Math., 72, pp.39~72 (1995)
  13. S. D. Kim, "On the exponential decay of C1 cubic Lagrange splines on non-uniform meshes and for non-uniform data points", Houston J. of Math., 24, pp.173~183 (1998)
  14. Y. Saad, "GMRES: A generalized minimal residual algorithm for solving nonsymmetric lienar systems", SIAM J. Sci. Comput., 7, pp.856~869 (1986)
  15. L. N. Trefethen, "Numerical linear algegra" (1997), SIAM

관련 논문AI추천

Error estimates of mixed finite element approximations for a class of fourth order elliptic control problemsTianliang Hou대한수학회 · 대한수학회보2013 · 제50권 제4호Error estimates of RT1 mixed methods for distributed optimal control problemsTianliang Hou대한수학회 · 대한수학회보2014 · 제51권 제1호A MULTIGRID METHOD FOR AN OPTIMAL CONTROL PROBLEM OF A DIFFUSION-CONVECTION EQUATION김상동, 백헌기, 이형천대한수학회 · 대한수학회지2010 · 제47권 제1호Preconditioners for a coupled problem by a penalty term arisen in an augmented Lagrangian method박은희, 이창옥대한수학회 · 대한수학회지2020 · 제57권 제5호Richardson extrapolation and defect correction of mixed finite element methods for elliptic optimal control problemsTianliang Hou, Yanping Chen, Yunqing Huang대한수학회 · 대한수학회지2012 · 제49권 제3호Preconditioned spectral collocation method on curved element domains using the Gordon-Hall transformation김상동, 신병천, HESSARIPEYMAN대한수학회 · 대한수학회보2014 · 제51권 제2호

이 간행물의 다른 논문 (9건)

Meromorphic Functions Sharing a Small Function with their Differential PolynomialsJilong Zhangpp. 345-355On Some Uniqueness Theorems of Meromorphic Functions Sharing Three ValuesPaulomi Chattopadhyay, Arindam Sarkarpp. 357-370Ostrowski's Type Inequalities for (α,m)-Convex FunctionsMuhamet Emin Ozdemir, Havva KavurmacI, Erhan Setpp. 371-378On Orthogonal Generalized (σ,τ )-Derivations of Semiprime Near-RingsShuliang Huangpp. 379-387On Some New Generalized Di erence Statistically Convergent Sequence Spaces De ned by a Sequence of Orlicz FunctionsCigdem Asma Bektas, Gulcan Aticipp. 389-397
원문 보기