Intrinsic scales and a posteriori multiscale error estimation for piecewise-linear functions and residuals

DOI10.1080/10618560600793497zbMath1134.65048OpenAlexW1974907147MaRDI QIDQ5442928

Guillermo Hauke, Mohamed H. Doweidar

Publication date: 18 February 2008

Published in: International Journal of Computational Fluid Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10618560600793497

zbMATH Keywords

numerical examplesfinite elementa posteriori error estimatorvariational multiscale methodone-dimensional transport equationone-dimensional advection-reaction equationone-dimensional diffusion-reaction equationpiecewise constant asymptotics

Mathematics Subject Classification ID

Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Linear boundary value problems for ordinary differential equations (34B05)

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Cites Work

• Unnamed Item
• Unnamed Item
• A relationship between stabilized finite element methods and the Galerkin method with bubble functions
• The variational multiscale method -- a paradigm for computational mechanics
• \(b=\int g\)
• Deriving upwinding, mass lumping and selective reduced integration by residual-free bubbles
• A posteriori error estimators for stationary convection-diffusion problems: A computational comparison
• A numerical study of a posteriori error estimators for convection-diffusion equations
• A simple subgrid scale stabilized method for the advection-diffusion-reaction equation
• On an improved unusual stabilized finite element method for the advective-reactive-diffusive equation
• The multiscale approach to error estimation and adaptivity
• Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods
• CHOOSING BUBBLES FOR ADVECTION-DIFFUSION PROBLEMS
• A POSTERIORI ERROR ESTIMATORS VIA BUBBLE FUNCTIONS