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Martin Vohralik - One of the best experts on this subject based on the ideXlab platform.

  • guaranteed and robust a posteriori error estimates for singularly perturbed reaction diffusion problems
    Mathematical Modelling and Numerical Analysis, 2009
    Co-Authors: Ibrahim Cheddadi, Radek Fucik, Mariana I Prieto, Martin Vohralik
    Abstract:

    We derive a posteriori error estimates for singularly perturbed reaction-diffusion problems which yield a guaranteed upper bound on the discretization error and are fully and easily computable. Moreover, they are also locally efficient and robust in the sense that they represent local lower bounds for the actual error, up to a generic constant independent in particular of the reaction coefficient. We present our results in the framework of the vertex-centered finite volume method but their nature is general for any conforming method, like the piecewise linear finite element one. Our estimates are based on a H(div)-conforming reconstruction of the Diffusive Flux in the lowest-order Raviart-Thomas space linked with mesh dual to the original simplicial one, previously introduced by the last author in the pure diffusion case. They also rely on elaborated Poincare, Friedrichs, and trace inequalities-based auxiliary estimates designed to cope optimally with the reaction dominance. In order to bring down the ratio of the estimated and actual overall energy error as close as possible to the optimal value of one, independently of the size of the reaction coefficient, we finally develop the ideas of local minimizations of the estimators by local modifications of the reconstructed Diffusive Flux. The numerical experiments presented confirm the guaranteed upper bound, robustness, and excellent efficiency of the derived estimates.

  • Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problems
    ESAIM: Mathematical Modelling and Numerical Analysis, 2009
    Co-Authors: Ibrahim Cheddadi, Radek Fucik, Mariana Prieto, Martin Vohralik
    Abstract:

    We derive a posteriori error estimates for singularly perturbed reaction-diffusion problems which yield a guaranteed upper bound on the discretization error and are fully and easily computable. Moreover, they are also locally efficient and robust in the sense that they represent local lower bounds for the actual error, up to a generic constant independent in particular of the reaction coefficient. We present our results in the framework of the vertex-centered finite volume method but their nature is general for any conforming method, like the piecewise linear finite element one. Our estimates are based on a H(div)-conforming reconstruction of the Diffusive Flux in the lowest-order Raviart-Thomas space linked with mesh dual to the original simplicial one, previously introduced by the last author in the pure diffusion case. They also rely on elaborated Poincaré, Friedrichs, and trace inequalities-based auxiliary estimates designed to cope optimally with the reaction dominance. In order to bring down the ratio of the estimated and actual overall energy error as close as possible to the optimal value of one, independently of the size of the reaction coefficient, we finally develop the ideas of local minimizations of the estimators by local modifications of the reconstructed Diffusive Flux. The numerical experiments presented confirm the guaranteed upper bound, robustness, and excellent efficiency of the derived estimates.

Ibrahim Cheddadi - One of the best experts on this subject based on the ideXlab platform.

  • guaranteed and robust a posteriori error estimates for singularly perturbed reaction diffusion problems
    Mathematical Modelling and Numerical Analysis, 2009
    Co-Authors: Ibrahim Cheddadi, Radek Fucik, Mariana I Prieto, Martin Vohralik
    Abstract:

    We derive a posteriori error estimates for singularly perturbed reaction-diffusion problems which yield a guaranteed upper bound on the discretization error and are fully and easily computable. Moreover, they are also locally efficient and robust in the sense that they represent local lower bounds for the actual error, up to a generic constant independent in particular of the reaction coefficient. We present our results in the framework of the vertex-centered finite volume method but their nature is general for any conforming method, like the piecewise linear finite element one. Our estimates are based on a H(div)-conforming reconstruction of the Diffusive Flux in the lowest-order Raviart-Thomas space linked with mesh dual to the original simplicial one, previously introduced by the last author in the pure diffusion case. They also rely on elaborated Poincare, Friedrichs, and trace inequalities-based auxiliary estimates designed to cope optimally with the reaction dominance. In order to bring down the ratio of the estimated and actual overall energy error as close as possible to the optimal value of one, independently of the size of the reaction coefficient, we finally develop the ideas of local minimizations of the estimators by local modifications of the reconstructed Diffusive Flux. The numerical experiments presented confirm the guaranteed upper bound, robustness, and excellent efficiency of the derived estimates.

  • Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problems
    ESAIM: Mathematical Modelling and Numerical Analysis, 2009
    Co-Authors: Ibrahim Cheddadi, Radek Fucik, Mariana Prieto, Martin Vohralik
    Abstract:

    We derive a posteriori error estimates for singularly perturbed reaction-diffusion problems which yield a guaranteed upper bound on the discretization error and are fully and easily computable. Moreover, they are also locally efficient and robust in the sense that they represent local lower bounds for the actual error, up to a generic constant independent in particular of the reaction coefficient. We present our results in the framework of the vertex-centered finite volume method but their nature is general for any conforming method, like the piecewise linear finite element one. Our estimates are based on a H(div)-conforming reconstruction of the Diffusive Flux in the lowest-order Raviart-Thomas space linked with mesh dual to the original simplicial one, previously introduced by the last author in the pure diffusion case. They also rely on elaborated Poincaré, Friedrichs, and trace inequalities-based auxiliary estimates designed to cope optimally with the reaction dominance. In order to bring down the ratio of the estimated and actual overall energy error as close as possible to the optimal value of one, independently of the size of the reaction coefficient, we finally develop the ideas of local minimizations of the estimators by local modifications of the reconstructed Diffusive Flux. The numerical experiments presented confirm the guaranteed upper bound, robustness, and excellent efficiency of the derived estimates.

Kim A. Anderson - One of the best experts on this subject based on the ideXlab platform.

  • Diffusive Flux of PAHs across sediment-water and water-air interfaces at urban superfund sites.
    Environmental Toxicology and Chemistry, 2017
    Co-Authors: D. James Minick, Kim A. Anderson
    Abstract:

    Superfund sites may be a source of polycyclic aromatic hydrocarbons (PAHs) to the surrounding environment. These sites can also act as PAH sinks from present day anthropogenic activities especially in urban locations. Understanding PAH transport across environmental compartments helps to define the relative contributions of these sources and is therefore important for informing remedial and management decisions. In the present study, paired passive samplers were co-deployed at sediment-water, and water-air interfaces within the Portland Harbor Superfund site (PHSS) and the McCormick and Baxter Superfund Site (MCBSS). These sites, located along the Willamette River in Portland, Oregon, have PAH contamination from both legacy and modern sources. Diffusive Flux calculations indicate that the Willamette River acts predominately as a sink for low molecular weight PAHs from both the sediment and the air. The sediment was also predominately a source of 4 and 5 ring PAHs to the river and the river was a source of these same PAHs to the air, indicating that legacy pollution may be contributing to PAH exposure for residents of the Portland urban center. At the remediated MCBSS Flux measurements highlight locations within the sand and rock sediment cap where contaminant breakthrough is occurring. This article is protected by copyright. All rights reserved

Mary Elizabeth Williams - One of the best experts on this subject based on the ideXlab platform.

  • Diffusive Flux of nanoparticles through chemically modified alumina membranes.
    The Analyst, 2011
    Co-Authors: Jason R. Stephens, Jacob S. Beveridge, Mary Elizabeth Williams
    Abstract:

    Surface chemistry plays an important role in determining Flux through porous media such as in the environment. In this paper Diffusive Flux of nanoparticles through alkylsilane modified porous alumina is measured as a model for understanding transport in porous media of differing surface chemistries. Experiments are performed as a function of particle size, pore diameter, attached hydrocarbon chain length and chain terminus, and solvent. Particle Fluxes are monitored by the change in absorbance of the solution in the receiving side of a diffusion cell. In general, Flux increases when the membranes are modified with alkylsilanes compared to untreated membranes, which is attributed to the hydrophobic nature of the porous membranes and differences in wettability. We find that Flux decreases, in both hexane and aqueous solutions, when the hydrocarbon chain lining the interior pore wall increases in length. The rate and selectivity of transport across these membranes is related to the partition coefficient (Kp) and the diffusion coefficient (D) of the permeating species. By conducting experiments as a function of initial particle concentration, we find that KpD increases with increasing particle size, is greater in alkylsilane–modified pores, and larger in hexane solution than water. The impact of the alkylsilane terminus (–CH3, –Br, –NH2, –COOH) on permeation in water is also examined. In water, the highest KpD is observed when the membranes are modified with carboxylic acid terminated silanes and lowest with amine terminated silanes as a result of electrostatic effects during translocation.

  • Diffusive Flux and magnetic manipulation of nanoparticles through porous membranes.
    Analytical chemistry, 2010
    Co-Authors: Jason R. Stephens, Jacob S. Beveridge, Andrew H. Latham, Mary Elizabeth Williams
    Abstract:

    Measurement of transport of nanometer scale particles through porous media is important to begin to understand the potential environmental impacts of nanomaterials. Using a diffusion cell with two compartments separated by either a porous alumina or polycarbonate membrane as a model system, Diffusive Flux through mesoporous materials is examined. Experiments are performed as a function of particle size, pore diameter, and solvent, and the particle Fluxes are monitored by the change in absorbance of the solution in the receiving cell. Using the measured extinction coefficient and change in absorbance of the solution as a function of time, the Fluxes of 3, 8, and 14 nm diameter CoFe2O4 particles are determined as they are translocated across pores with diameters 30, 50, 100, and 200 nm in hexane and aqueous solutions. In general, Flux decreases with increasing particle size and increases with pore diameter. We find that Fluxes are faster in aqueous solutions than in hexane, which is attributed to the hydrop...

Benson T Jung - One of the best experts on this subject based on the ideXlab platform.