Maximum norm a posteriori error estimate for a 3d singularly perturbed semilinear reaction-diffusion problem

Advances in Computational Mathematics ◽

10.1007/s10444-010-9163-2 ◽

2010 ◽

Vol 35 (1) ◽

pp. 33-55 ◽

Author(s):

Naresh M. Chadha ◽

Natalia Kopteva

Keyword(s):

Error Estimate ◽

Reaction Diffusion ◽

Posteriori Error ◽

Diffusion Problem ◽

A Posteriori Error Estimate ◽

Singularly Perturbed ◽

Maximum Norm ◽

Posteriori Error Estimate ◽

A Posteriori ◽

A Posteriori Error

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Maximum Norm A Posteriori Error Estimate for a 2D Singularly Perturbed Semilinear Reaction-Diffusion Problem

SIAM Journal on Numerical Analysis ◽

10.1137/060677616 ◽

2008 ◽

Vol 46 (3) ◽

pp. 1602-1618 ◽

Author(s):

Natalia Kopteva

Keyword(s):

Error Estimate ◽

Reaction Diffusion ◽

Posteriori Error ◽

Diffusion Problem ◽

A Posteriori Error Estimate ◽

Singularly Perturbed ◽

Maximum Norm ◽

Posteriori Error Estimate ◽

A Posteriori ◽

A Posteriori Error

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Maximum norm a posteriori error estimates for a 1D singularly perturbed semilinear reaction-diffusion problem

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drl020 ◽

2006 ◽

Vol 27 (3) ◽

pp. 576-592 ◽

Author(s):

N. Kopteva

Keyword(s):

Error Estimates ◽

A Posteriori Error Estimates ◽

Reaction Diffusion ◽

Posteriori Error ◽

Diffusion Problem ◽

Singularly Perturbed ◽

Maximum Norm ◽

A Posteriori ◽

A Posteriori Error

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A posteriori error estimate for finite volume approximations to singularly perturbed nonlinear convection-diffusion equations

Numerische Mathematik ◽

10.1007/pl00005431 ◽

2001 ◽

Vol 87 (4) ◽

pp. 737-761 ◽

Author(s):

Mario Ohlberger

Keyword(s):

Error Estimate ◽

Posteriori Error ◽

A Posteriori Error Estimate ◽

Singularly Perturbed ◽

Diffusion Equations ◽

Posteriori Error Estimate ◽

A Posteriori ◽

Nonlinear Convection ◽

A Posteriori Error ◽

Convection Diffusion

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An a posteriori error estimate for finite element approximations of a singularly perturbed advection-diffusion problem

Journal of Computational and Applied Mathematics ◽

10.1016/s0377-0427(97)00191-x ◽

1997 ◽

Vol 87 (2) ◽

pp. 227-242 ◽

Author(s):

Song Wang

Keyword(s):

Finite Element ◽

Posteriori Error ◽

Diffusion Problem ◽

A Posteriori Error Estimate ◽

Singularly Perturbed ◽

Posteriori Error Estimate ◽

A Posteriori ◽

A Posteriori Error ◽

Finite Element Approximations ◽

Advection Diffusion

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An anisotropic a-posteriori error estimate for a convection-diffusion problem

Computing and Visualization in Science ◽

10.1007/s007910100061 ◽

2001 ◽

Vol 4 (2) ◽

pp. 99-104 ◽

Author(s):

Luca Formaggia ◽

Simona Perotto ◽

Paolo Zunino

Keyword(s):

Error Estimate ◽

Posteriori Error ◽

Diffusion Problem ◽

A Posteriori Error Estimate ◽

Posteriori Error Estimate ◽

A Posteriori ◽

A Posteriori Error ◽

Convection Diffusion

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A new a posteriori error estimate for convection–reaction–diffusion problems

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2007.04.033 ◽

2008 ◽

Vol 218 (1) ◽

pp. 70-78 ◽

Author(s):

Dmitri Kuzmin ◽

Antti Hannukainen ◽

Sergey Korotov

Keyword(s):

Error Estimate ◽

Reaction Diffusion ◽

Posteriori Error ◽

A Posteriori Error Estimate ◽

Posteriori Error Estimate ◽

A Posteriori ◽

A Posteriori Error ◽

Diffusion Problems

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Functional A Posteriori Error Estimate for a Nonsymmetric Stationary Diffusion Problem

Computational Methods in Applied Sciences - Mathematical Modeling and Optimization of Complex Structures ◽

10.1007/978-3-319-23564-6_2 ◽

2015 ◽

pp. 21-30

Author(s):

Olli Mali

Keyword(s):

Error Estimate ◽

Posteriori Error ◽

Diffusion Problem ◽

A Posteriori Error Estimate ◽

Posteriori Error Estimate ◽

A Posteriori ◽

A Posteriori Error ◽

Stationary Diffusion

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A multiscale a posteriori error estimate

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2004.07.012 ◽

2005 ◽

Vol 194 (18-20) ◽

pp. 2077-2094 ◽

Author(s):

Rodolfo Araya ◽

Frédéric Valentin

Keyword(s):

Error Estimate ◽

Posteriori Error ◽

A Posteriori Error Estimate ◽

Posteriori Error Estimate ◽

A Posteriori ◽

A Posteriori Error

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Guaranteed a posteriori error estimates for nonconforming finite element approximations to a singularly perturbed reaction–diffusion problem

Applied Numerical Mathematics ◽

10.1016/j.apnum.2015.02.002 ◽

2015 ◽

Vol 94 ◽

pp. 1-15 ◽

Author(s):

Bei Zhang ◽

Shaochun Chen ◽

Jikun Zhao

Keyword(s):

Finite Element ◽

A Posteriori Error Estimates ◽

Reaction Diffusion ◽

Posteriori Error ◽

Diffusion Problem ◽

Singularly Perturbed ◽

Nonconforming Finite Element ◽

A Posteriori ◽

A Posteriori Error ◽

Finite Element Approximations

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A HIERARCHICAL A POSTERIORI ERROR ESTIMATE FOR AN ADVECTION-DIFFUSION-REACTION PROBLEM

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202505000674 ◽

2005 ◽

Vol 15 (07) ◽

pp. 1119-1139 ◽

Author(s):

RODOLFO ARAYA ◽

ABNER H. POZA ◽

ERNST P. STEPHAN

Keyword(s):

Error Estimate ◽

Posteriori Error ◽

A Posteriori Error Estimate ◽

Diffusion Reaction ◽

Posteriori Error Estimate ◽

A Posteriori ◽

A Posteriori Error ◽

Advection Diffusion ◽

Norm Of The Error ◽

Reaction Problem

In this work we introduce a new a posteriori error estimate of hierarchical type for the advection-diffusion-reaction equation. We prove the equivalence between the energy norm of the error and our error estimate using an auxiliary linear problem for the residual and an easy way to prove inf–sup condition.

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