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Adaptive Discontinuous Galerkin Methods for Non-linear Reactive Flows

  • Book
  • © 2016

Overview

Authors:
  1. Murat Uzunca

    1. Institute of Applied Mathematics, Middle East Technical University Institute of Applied Mathematics, Ankara, Türkiye

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  • A unified description of space-time adaptive
  • discontinuous Galerkin methods for nonlinear reactive flows
  • Highly accurate resolution of interior and
  • boundary layers in advection dominated
  • Applications in contaminant flow, biodegradiation, flow in heterogeneous porous and fractured media

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    • Murat Uzunca
    Pages 1-7

  3. Discontinuous Galerkin Methods

    • Murat Uzunca
    Pages 9-25

  4. Elliptic Problems with Adaptivity

    • Murat Uzunca
    Pages 27-56

  5. Parabolic Problems with Space-Time Adaptivity

    • Murat Uzunca
    Pages 57-81

  6. Conclusions and Outline

    • Murat Uzunca
    Pages 83-84

  7. Back Matter

    Pages 85-105
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Keywords

About this book

The focus of this monograph is the development of space-time adaptive methods to solve the convection/reaction dominated non-stationary semi-linear advection diffusion reaction (ADR) equations with internal/boundary layers in an accurate and efficient way.  After introducing the ADR equations and discontinuous Galerkin discretization, robust residual-based a posteriori error estimators in space and time are derived. The elliptic reconstruction technique is then utilized to derive the a posteriori error bounds for the fully discrete system and to obtain optimal orders of convergence.
As coupled surface and subsurface flow over large space and time scales is described by (ADR) equation the methods described in this book are of high importance in many areas of Geosciences including oil and gas recovery, groundwater contamination and sustainable use of groundwater resources, storing greenhouse gases or radioactive waste in the subsurface.


Authors and Affiliations

  • Institute of Applied Mathematics, Middle East Technical University Institute of Applied Mathematics, Ankara, Türkiye

    Murat Uzunca

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