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Adaptive Discontinuous Galerkin Methods for Non-linear Reactive Flows

Adaptive Discontinuous Galerkin Methods for Non-linear Reactive Flows by Murat Uzunca
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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.

Springer International Publishing; May 2016
111 pages; ISBN 9783319301303
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Title: Adaptive Discontinuous Galerkin Methods for Non-linear Reactive Flows
Author: Murat Uzunca
 
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