Error Estimate for the Finite Volume Approximate of the Solution to a Nonlinear Convective Equation

Eymard, Robert; Gallouët, Thierry; Ghilani, Mustapha; Herbin, Raphaèle

doi:10.1007/978-94-017-2856-0_2

Cited by 10 publications

(13 citation statements)

References 1 publication

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“…It is immediate by inspection that the stabilisation operators defined in sections 2.2 and 2.3 both define the semi-norm (21). Now define the semi-norm for discrete stability…”

Section: Satisfaction Of the Assumptions For The Methods Discussedmentioning

confidence: 99%

Stabilised Finite Element Methods for Ill-Posed Problems with Conditional Stability

Burman

2016

Lecture Notes in Computational Science and Engineering

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In this paper we discuss the adjoint stabilised finite element method introduced in E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive and ill-posed problems. Part I: elliptic equations, SIAM Journal on Scientific Computing [10] and how it may be used for the computation of solutions to problems for which the standard stability theory given by the Lax-Milgram Lemma or the Babuska-Brezzi Theorem fails. We pay particular attention to ill-posed problems that have some conditional stability property and prove (conditional) error estimates in an abstract framework. As a model problem we consider the elliptic Cauchy problem and provide a complete numerical analysis for this case. Some numerical examples are given to illustrate the theory.

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“…It is immediate by inspection that the stabilisation operators defined in sections 2.2 and 2.3 both define the semi-norm (21). Now define the semi-norm for discrete stability…”

Section: Satisfaction Of the Assumptions For The Methods Discussedmentioning

confidence: 99%

Stabilised Finite Element Methods for Ill-Posed Problems with Conditional Stability

Burman

2016

Lecture Notes in Computational Science and Engineering

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“…have recently been obtained. Indeed, Evje and Karlsen (2002) proved that and Eymard, Gallouët and Herbin (2002a) proved that…”

Section: A Priori Error Estimates IVmentioning

confidence: 98%

Continuous dependence and error estimation for viscosity methods

Cockburn

2003

Acta Numerica

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In this paper, we review some ideas on continuous dependence results for the entropy solution of hyperbolic scalar conservation laws. They lead to a complete L^\infty(L^1)-approximation theory with which error estimates for numerical methods for this type of equation can be obtained. The approach we consider consists in obtaining continuous dependence results for the solutions of parabolic conservation laws and deducing from them the corresponding results for the entropy solution. This is a natural approach, as the entropy solution is nothing but the limit of solutions of parabolic scalar conservation laws as the viscosity coefficient goes to zero.

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“…1). These meshes are called admissible meshes and were proposed by Herbin [4,5]. The advantage of such meshes is that they allow the use of simple schemes for the discretization of ðr/Þ P k Áñ P k .…”

Section: Introductionmentioning

confidence: 98%

A robust and efficient finite volume scheme for the discretization of diffusive flux on extremely skewed meshes in complex geometries

Traoré

Ahipo

Louste

2009

Journal of Computational Physics

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Error Estimate for the Finite Volume Approximate of the Solution to a Nonlinear Convective Equation

Cited by 10 publications

References 1 publication

Stabilised Finite Element Methods for Ill-Posed Problems with Conditional Stability

Stabilised Finite Element Methods for Ill-Posed Problems with Conditional Stability

Continuous dependence and error estimation for viscosity methods

A robust and efficient finite volume scheme for the discretization of diffusive flux on extremely skewed meshes in complex geometries

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