Explicit and averaging a posteriori error estimates for adaptive finite volume methods Academic Article

abstract

• Local mesh-refining algorithms known from adaptive finite element methods are adopted for locally conservative and monotone finite volume discretizations of boundary value problems for steady-state convection-diffusion-reaction equations. The paper establishes residual-type explicit error estimators and averaging techniques for a posteriori finite volume error control with and without upwind in global H 1- and L 2-norms. Reliability and efficiency are verified theoretically and confirmed empirically with experimental support for the superiority of the suggested adaptive mesh-refining algorithms over uniform mesh refining. A discussion of adaptive computations in the simulation of contaminant concentration in a nonhomogeneous water reservoir concludes the paper. 2005 Society for Industrial and Applied Mathematics.

authors

• Lazarov, Raytcho

published proceedings

• SIAM JOURNAL ON NUMERICAL ANALYSIS

author list (cited authors)

• Carstensen, C., Lazarov, R., & Tomov, S.

citation count

• 39

complete list of authors

• Carstensen, C||Lazarov, R||Tomov, S

publication date

• January 2005

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

published in

• SIAM Journal on Numerical Analysis  Journal

keywords

• 3-d Problems
• A Posteriori Error Estimators
• Averaging Estimators
• Convection-diffusion-reaction Equations
• Finite Volume Approximation
• Residual Estimators
• Zz Refinement Indicator

Digital Object Identifier (DOI)

• 10.1137/S0036142903425422

URI

• https://hdl.handle.net/1969.1/183697

start page

• 2496

end page

• 2521

volume

• 42

issue

• 6

URL

• http://dx.doi.org/10.1137/s0036142903425422