Adaptive Discontinuous Galerkin Methods for Non-linear Reactive Flows
Published on 17. May 2016
IX, 105 pages
978-3-319-30130-3 (ISBN)
Description
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.
More details
Series
Edition
1st ed. 2016
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
IX, 105 p. 38 illus., 10 illus. in color.
File size
3,07 MB
ISBN-13
978-3-319-30130-3 (9783319301303)
DOI
10.1007/978-3-319-30130-3
Schweitzer Classification
Other editions
Additional editions
Book
05/2016
Birkhäuser
€53.49
Shipment within 10-15 days
Content
1 INTRODUCTION.- 1.1 Geological and computational background.- 1.2 Outline.- 2 DISCONTINUOUS GALERKIN METHODS.- 2.1 Preliminaries.- 2.2 Construction of IPG Methods.- 2.3 Computation Tools for Integral Terms.- 2.4 Effect of Penalty Parameter.- 2.5 Problems with Convection.- 3 ELLIPTIC PROBLEMS WITH ADAPTIVITY.- 3.1 Model Elliptic Problem.- 3.2 Adaptivity.- 3.3 Solution of Linearized Systems.- 3.4 Comparison with Galerkin Least Squares FEM (GLSFEM).- 3.5 Numerical Examples.- 4 PARABOLIC PROBLEMS WITH TIME-SPACE ADAPTIVITY.- 4.1 Preliminaries and Model Equation.- 4.2 Semi-Discrete and Fully Discrete Formulations.- 4.3 Time-Space Adaptivity for Non-Stationary Problems.- 4.4 Solution of Fully Discrete System.- 4.5 Numerical Examples.-REFERENCES.
