Error estimates for the combinedh andp versions of the finite element method
作者： Ivo Babuška , Milo R. Dorr
DOI: 10.1007/BF01398256
关键词: Geometry 、 Finite element method 、 hp-FEM 、 Numerical analysis 、 Rate of convergence 、 Polynomial 、 Degrees of freedom 、 Convergence (routing) 、 Mathematics 、 Degree (graph theory) 、 Applied mathematics 、 Computational mathematics
摘要: In theh-version of the finite element method, convergence is achieved by refining mesh while keeping degree elements fixed. On other hand, thep-version keeps fixed and increases elements. this paper, we prove estimates showing simultaneous dependence order approximation on both degrees mesh. addition, it shown that a proper design distribution lead to better than polynomial rate with respect number freedom, even in presence corner singularities. Numerical results comparing theh-version,p-version, combinedh-p-version for one dimensional problem are presented.
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sci-hub.se 参考文章(8)
R. DeVore, K. Scherer, VARIABLE KNOT, VARIABLE DEGREE SPLINE APPROXIMATION TO Xβ Quantitative Approximation#R##N#Proceedings of a Symposium on Quantitative Approximation Held in Bonn, West Germany, August 20–24, 1979. pp. 121- 131 ,(1980) , 10.1016/B978-0-12-213650-4.50016-7
Elias M. Stein, Singular Integrals and Differentiability Properties of Functions. ,(1971)
Pierre Grisvard, Boundary value problems in non-smooth domains University of Maryland, Dept. of Mathematics. ,(1980)
Philippe G. Ciarlet, J. T. Oden, The Finite Element Method for Elliptic Problems ,(1978)
Olof Widlund, On best error bounds for approximation by piecewise polynomial functions Numerische Mathematik. ,vol. 27, pp. 327- 338 ,(1976) , 10.1007/BF01396181
R. B. Kellogg, J. Pitkäranta, I. Babuška, Direct and inverse error estimates for finite elements with mesh refinements Numerische Mathematik. ,vol. 33, pp. 447- 471 ,(1979) , 10.1007/BF01399326
V. A. Kondrat'ev, Boundary problems for elliptic equations in domains with conical or angular points Trans. Moscow Math. Soc.. ,vol. 16, pp. 227- 313 ,(1967)
Babuska, Szabo, Katz, The p -Version of the Finite Element Method ,(1981)