Boundary augmented Lagrangian method for the Signorini problem

Zhang, Shougui; Li, Xin

doi:10.1007/s10492-016-0129-7

Cited by 3 publications

(2 citation statements)

References 27 publications

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“…The finite difference method (FDM) [3], [20], [22], the finite element method (FEM) [11] and the boundary element method (BEM) [7], [23] can be employed to obtain approximate solutions of hyperbolic problems. In these methods, the precision of approximate solutions relies acutely on the quality of meshes or elements.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of the meshless element-free Galerkin method for hyperbolic initial-boundary value problems

Tang

2017

Appl.Math.

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Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz 62 (2017) APPLICATIONS OF MATHEMATICS No. 5, 477-492

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Section: Introductionmentioning

confidence: 99%

Numerical analysis of the meshless element-free Galerkin method for hyperbolic initial-boundary value problems

Tang

2017

Appl.Math.

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“…with various boundary values [7], mechanics [7] [8] [9], medical imaging and computational biology [10], geophysics [11], ontology regarding big data representation and storage [12], and elastica theory [13], to name just a few.…”

Section: Introductionmentioning

confidence: 99%

Augmented Lagrangian Methods for Numerical Solutions to Higher Order Differential Equations

Li¹

2017

JAMP

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A large number of problems in engineering can be formulated as the optimization of certain functionals. In this paper, we present an algorithm that uses the augmented Lagrangian methods for finding numerical solutions to engineering problems. These engineering problems are described by differential equations with boundary values and are formulated as optimization of some functionals. The algorithm achieves its simplicity and versatility by choosing linear equality relations recursively for the augmented Lagrangian associated with an optimization problem. We demonstrate the formulation of an optimization functional for a 4th order nonlinear differential equation with boundary values. We also derive the associated augmented Lagrangian for this 4th order differential equation. Numerical test results are included that match up with well-established experimental outcomes. These numerical results indicate that the new algorithm is fully capable of producing accurate and stable solutions to differential equations.

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Projection and self-adaptive projection methods for the Signorini problem with the BEM

Zhang

2017

Computers & Mathematics with Applications

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Boundary augmented Lagrangian method for the Signorini problem

Abstract: Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Cited by 3 publications

References 27 publications

Numerical analysis of the meshless element-free Galerkin method for hyperbolic initial-boundary value problems

Numerical analysis of the meshless element-free Galerkin method for hyperbolic initial-boundary value problems

Augmented Lagrangian Methods for Numerical Solutions to Higher Order Differential Equations

Projection and self-adaptive projection methods for the Signorini problem with the BEM

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