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Moving Mesh Finite Element Methods for an Optimal Control Problem for the Advection-Diffusion Equation

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Abstract

An optimal control problem for the advection-diffusion equation is studied using a Lagrangian-moving mesh finite element method. The weak formulation of the model advection–diffusion equation is based on Lagrangian coordinates, and semi–discrete (in space) error estimates are derived under minimal regularity assumptions. In addition, using these estimates and Brezzi-Rappaz-Raviart theory, symmetric error estimates for the optimality system are derived. The results also apply for advection dominated problems

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  1. Konstantinos Chrysafinos

    Present address: Institut für Numerische Simulation, Universität Bonn, Wegelerstr 6, Bonn, 53115, Germany

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  1. Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Konstantinos Chrysafinos

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  1. Konstantinos Chrysafinos
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Correspondence to Konstantinos Chrysafinos.

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Chrysafinos, K. Moving Mesh Finite Element Methods for an Optimal Control Problem for the Advection-Diffusion Equation. J Sci Comput 25, 401–421 (2005). https://doi.org/10.1007/s10915-004-4804-6

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  • DOI: https://doi.org/10.1007/s10915-004-4804-6

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