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A primal-dual integral method in global optimization

Jens Hichert, Armin Hoffmann, Huan Xoang Phú, Rüdiger Reinhardt (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Using the Fenchel conjugate F c of Phú’s Volume function F of a given essentially bounded measurable function f defined on the bounded box D ⊂ Rⁿ, the integral method of Chew and Zheng for global optimization is modified to a superlinearly convergent method with respect to the level sequence. Numerical results are given for low dimensional functions with a strict global essential supremum.

A priori convergence of the greedy algorithm for the parametrized reduced basis method

Annalisa Buffa, Yvon Maday, Anthony T. Patera, Christophe Prud’homme, Gabriel Turinici (2012)

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

The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the a priori convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we...

A priori convergence of the Greedy algorithm for the parametrized reduced basis method

Annalisa Buffa, Yvon Maday, Anthony T. Patera, Christophe Prud’homme, Gabriel Turinici (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the a priori convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we...

A priori convergence of the Greedy algorithm for the parametrized reduced basis method

Annalisa Buffa, Yvon Maday, Anthony T. Patera, Christophe Prud’homme, Gabriel Turinici (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the a priori convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we...

A priori error analysis of a fully-mixed finite element method for a two-dimensional fluid-solid interaction problem

Carolina Domínguez, Gabriel N. Gatica, Salim Meddahi, Ricardo Oyarzúa (2013)

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

We introduce and analyze a fully-mixed finite element method for a fluid-solid interaction problem in 2D. The model consists of an elastic body which is subject to a given incident wave that travels in the fluid surrounding it. Actually, the fluid is supposed to occupy an annular region, and hence a Robin boundary condition imitating the behavior of the scattered field at infinity is imposed on its exterior boundary, which is located far from the obstacle. The media are governed by the elastodynamic...

A priori error estimates for a state-constrained elliptic optimal control problem

Arnd Rösch, Simeon Steinig (2012)

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

We examine an elliptic optimal control problem with control and state constraints in ℝ3. An improved error estimate of 𝒪(hs) with 3/4 ≤ s ≤ 1 − ε is proven for a discretisation involving piecewise constant functions for the control and piecewise linear for the state. The derived order of convergence is illustrated by a numerical example.

A priori error estimates for a state-constrained elliptic optimal control problem

Arnd Rösch, Simeon Steinig (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We examine an elliptic optimal control problem with control and state constraints in ℝ3. An improved error estimate of 𝒪(hs) with 3/4 ≤ s ≤ 1 − ε is proven for a discretisation involving piecewise constant functions for the control and piecewise linear for the state. The derived order of convergence is illustrated by a numerical example.

A priori error estimates for a state-constrained elliptic optimal control problem

Arnd Rösch, Simeon Steinig (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We examine an elliptic optimal control problem with control and state constraints in ℝ3. An improved error estimate of 𝒪(hs) with 3/4 ≤ s ≤ 1 − ε is proven for a discretisation involving piecewise constant functions for the control and piecewise linear for the state. The derived order of convergence is illustrated by a numerical example.

A priori error estimates for finite element discretizations of a shape optimization problem

Bernhard Kiniger, Boris Vexler (2013)

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

In this paper we consider a model shape optimization problem. The state variable solves an elliptic equation on a domain with one part of the boundary described as the graph of a control function. We prove higher regularity of the control and develop a priori error analysis for the finite element discretization of the shape optimization problem under consideration. The derived a priori error estimates are illustrated on two numerical examples.

A priori error estimates for Lagrange interpolation on triangles

Kenta Kobayashi, Takuya Tsuchiya (2015)

Applications of Mathematics

We present the error analysis of Lagrange interpolation on triangles. A new a priori error estimate is derived in which the bound is expressed in terms of the diameter and circumradius of a triangle. No geometric conditions on triangles are imposed in order to get this type of error estimates. To derive the new error estimate, we make use of the two key observations. The first is that squeezing a right isosceles triangle perpendicularly does not reduce the approximation property of Lagrange interpolation....

A priori error estimates for reduced order models in finance

Ekkehard W. Sachs, Matthias Schu (2013)

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

Mathematical models for option pricing often result in partial differential equations. Recent enhancements are models driven by Lévy processes, which lead to a partial differential equation with an additional integral term. In the context of model calibration, these partial integro differential equations need to be solved quite frequently. To reduce the computational cost the implementation of a reduced order model has shown to be very successful numerically. In this paper we give a priori error...

Currently displaying 821 – 840 of 1956