The numerical solution of Newton's problem of least resistance

DOI10.1007/s10107-014-0756-2zbMath1301.65054OpenAlexW2074285813MaRDI QIDQ463735

Gerd Wachsmuth

Publication date: 17 October 2014

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10107-014-0756-2

zbMATH Keywords

variational problemnumerical examplesEuler-Lagrange equationNewton's problemconcave solutionconvex body of least resistance

Mathematics Subject Classification ID

Computational aspects related to convexity (52B55) Numerical optimization and variational techniques (65K10) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items (11)

Adaptive, anisotropic and hierarchical cones of discrete convex functions ⋮ Local properties of the surface measure of convex bodies ⋮ A solution to Newton's least resistance problem is uniquely defined by its singular set ⋮ On generalized Newton’s aerodynamic problem ⋮ Conforming approximation of convex functions with the finite element method ⋮ The analytical solution of Newton’s aerodynamic problem in the class of bodies with vertical plane of symmetry and developable side boundary ⋮ On the structure of singular points of a solution to Newton's least resistance problem ⋮ A note on Newton's problem of minimal resistance for convex bodies ⋮ Hessian measures in the aerodynamic Newton problem ⋮ Non-optimality of conical parts for Newton's problem of minimal resistance in the class of convex bodies and the limiting case of infinite height ⋮ Method of nose stretching in Newton’s problem of minimal resistance

Uses Software

• CGAL
• 2D triangulations

Cites Work

• Unnamed Item
• Approximating optimization problems over convex functions
• On Newton's problem of minimal resistance
• An algorithm for computing solutions of variational problems with global convexity constraints
• H1-projection into the set of convex functions : a saddle-point formulation
• Newton's Problem of the Body of Minimal Resistance in the Class of Convex Developable Functions
• On Convex Functions and the Finite Element Method
• Minimum Problems over Sets of Concave Functions and Related Questions
• A Numerical Method for Variational Problems with Convexity Constraints
• Minimizing within Convex Bodies Using a Convex Hull Method
• A symmetry problem in the calculus of variations
• A numerical approach to variational problems subject to convexity constraint

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