Fully Discrete Analysis of a Discontinuous Finite Element Method for the Keller-Segel Chemotaxis Model

Authors:
Yekaterina Epshteyn;Ahmet Izmirlioglu
Affiliations:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, USA 15213;Department of Mathematics, University of Pittsburgh, Pittsburgh, USA 15260
Venue:
Journal of Scientific Computing
Year:
2009

Citing 12
Cited 4

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Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton--Jacobi Equations

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Error Estimates to Smooth Solutions of Runge--Kutta Discontinuous Galerkin Methods for Scalar Conservation Laws

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A finite volume scheme for the Patlak–Keller–Segel chemotaxis model

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A Note on Discontinuous Galerkin Divergence-free Solutions of the Navier-Stokes Equations

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Discontinuous Galerkin methods for the chemotaxis and haptotaxis models

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A second-order positivity preserving central-upwind scheme for chemotaxis and haptotaxis models

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New Interior Penalty Discontinuous Galerkin Methods for the Keller-Segel Chemotaxis Model

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Foreword

Journal of Scientific Computing
Finite volume methods for degenerate chemotaxis model

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Upwind-Difference Potentials Method for Patlak-Keller-Segel Chemotaxis Model

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Nonnegativity of exact and numerical solutions of some chemotactic models

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Abstract

This paper formulates and analyzes fully discrete schemes for the two-dimensional Keller-Segel chemotaxis model. The spatial discretization of the model is based on the discontinuous Galerkin methods and the temporal discretization is based either on Forward Euler or the second order explicit total variation diminishing (TVD) Runge-Kutta methods. We consider Cartesian grids and prove fully discrete error estimates for the proposed methods. Our proof is valid for pre-blow-up times since we assume boundedness of the exact solution.