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The descent algorithms for solving symmetric Pareto eigenvalue complementarity problem

Lu Zou, Yuan Lei (2023)

Applications of Mathematics

For the symmetric Pareto Eigenvalue Complementarity Problem (EiCP), by reformulating it as a constrained optimization problem on a differentiable Rayleigh quotient function, we present a class of descent methods and prove their convergence. The main features include: using nonlinear complementarity functions (NCP functions) and Rayleigh quotient gradient as the descent direction, and determining the step size with exact linear search. In addition, these algorithms are further extended to solve the...

The discrete compactness property for anisotropic edge elements on polyhedral domains

Ariel Luis Lombardi (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We prove the discrete compactness property of the edge elements of any order on a class of anisotropically refined meshes on polyhedral domains. The meshes, made up of tetrahedra, have been introduced in [Th. Apel and S. Nicaise, Math. Meth. Appl. Sci. 21 (1998) 519–549]. They are appropriately graded near singular corners and edges of the polyhedron.

The discrete compactness property for anisotropic edge elements on polyhedral domains∗

Ariel Luis Lombardi (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We prove the discrete compactness property of the edge elements of any order on a class of anisotropically refined meshes on polyhedral domains. The meshes, made up of tetrahedra, have been introduced in [Th. Apel and S. Nicaise, Math. Meth. Appl. Sci. 21 (1998) 519–549]. They are appropriately graded near singular corners and edges of the polyhedron.

The discrete maximum principle for Galerkin solutions of elliptic problems

Tomáš Vejchodský (2012)

Open Mathematics

This paper provides an equivalent characterization of the discrete maximum principle for Galerkin solutions of general linear elliptic problems. The characterization is formulated in terms of the discrete Green’s function and the elliptic projection of the boundary data. This general concept is applied to the analysis of the discrete maximum principle for the higher-order finite elements in one-dimension and to the lowest-order finite elements on simplices of arbitrary dimension. The paper surveys...

The distance of a curve to its control polygon.

Jesús Miguel Carnicer, M.S. Floater, Juan M. Peña (2002)

RACSAM

Recientemente, Nairn, Peters y Lutterkort han acotado la distancia entre una curva de Bézier y su polígono de control en términos de las diferencias entre los puntos de control. Mostramos cómo extender dichas cotas a muchos tipos de curvas utilizadas en el Diseño Geométrico.

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