Adaptive Discontinuous Galerkin Methods for Non-linear Reactive Flows

✍ Scribed by Murat Uzunca (auth.)

• Publisher: Birkhäuser Basel
• Year: 2016
• Tongue: English
• Leaves: 111
• Series: Lecture Notes in Geosystems Mathematics and Computing
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-ix
Introduction....Pages 1-7
Discontinuous Galerkin Methods....Pages 9-25
Elliptic Problems with Adaptivity....Pages 27-56
Parabolic Problems with Space-Time Adaptivity....Pages 57-81
Conclusions and Outline....Pages 83-84
Back Matter....Pages 85-105

✦ Subjects

Numerical Analysis;Partial Differential Equations;Geophysics/Geodesy