A Numerical Method Based on Higher Order Polynomial Approximation for Second Order Elliptic Eigenvalue Problems on Arbitrary Convex Quadrilateral Domain

2021 ◽  
Vol 10 (12) ◽  
pp. 4201-4208
Author(s):  
继会 郑
Keyword(s):  
Numerical Method ◽  
Polynomial Approximation ◽  
Eigenvalue Problems ◽  
Higher Order ◽  
Second Order ◽  
Convex Quadrilateral ◽  
Order Polynomial ◽  
Arbitrary Convex ◽  
Elliptic Eigenvalue Problems

scholarly journals Pointwise estimates for higher order convexity preserving polynomial approximation

1994 ◽  
Vol 36 (2) ◽  
pp. 213-233 ◽  
Author(s):  
Jia-Ding Cao ◽  
Heinz H. Gonska
Keyword(s):  
Polynomial Approximation ◽  
Convex Functions ◽  
Higher Order ◽  
Second Order ◽  
Convolution Type ◽  
Shape Preservation ◽  
Moduli Of Continuity ◽  
Pointwise Estimates ◽  
Higher Order Convexity ◽  
Boolean Sum

AbstractDeVore-Gopengauz-type operators have attracted some interest over the recent years. Here we investigate their relationship to shape preservation. We construct certain positive convolution-type operators Hn, s, j which leave the cones of j-convex functions invariant and give Timan-type inequalities for these. We also consider Boolean sum modifications of the operators Hn, s, j show that they basically have the same shape preservation behavior while interpolating at the endpoints of [−1, 1], and also satisfy Telyakovskiῐ- and DeVore-Gopengauz-type inequalities involving the first and second order moduli of continuity, respectively. Our results thus generalize related results by Lorentz and Zeller, Shvedov, Beatson, DeVore, Yu and Leviatan.

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