Introduction / 1: |
Challenges and motivation / 1.1: |
Literature review / 1.2: |
Overview of the content of the book / 1.3: |
Multiscale finite element methods for linear problems and overview / 2: |
Summary / 2.1: |
Introduction to multiscale finite element methods / 2.2: |
Reducing boundary effects / 2.3: |
Motivation / 2.3.1: |
Oversampling technique / 2.3.2: |
Generalization of MsFEM: A look forward / 2.4: |
Brief overview of various global couplings of multiscale basis functions / 2.5: |
Multiscale finite volume (MsFV) and multiscale finite volume element method (MsFVEM) / 2.5.1: |
Mixed multiscale finite element method / 2.5.2: |
MsFEM for problems with scale separation / 2.6: |
Extension of MsFEM to parabolic problems / 2.7: |
Comparison to other multiscale methods / 2.8: |
Performance and implementation issues / 2.9: |
Cost and performance / 2.9.1: |
Convergence and accuracy / 2.9.2: |
Coarse-grid choice / 2.9.3: |
An application to two-phase flow / 2.10: |
Discussions / 2.11: |
Multiscale finite element methods for nonlinear equations / 3: |
MsFEM for nonlinear problems. Introduction / 3.1: |
Multiscale finite volume element method (MsFVEM) / 3.2: |
Examples of Ph / 3.3: |
Relation to upscaling methods / 3.4: |
Multiscale finite element methods for nonlinear parabolic equations / 3.5: |
Summary of convergence of MsFEM for nonlinear partial differential equations / 3.6: |
Numerical results / 3.7: |
Multiscale finite element methods using limited global information / 3.8: |
A motivating numerical example / 4.1: |
Mixed multiscale finite element methods using limited global information / 4.2: |
Elliptic equations / 4.2.1: |
Parabolic equations / 4.2.2: |
Galerkin multiscale finite element methods using limited global information / 4.2.3: |
A special case / 4.3.1: |
General case / 4.3.2: |
The use of approximate global information / 4.3.3: |
Iterative MsFEM / 4.4.1: |
Applications of multiscale finite element methods / 4.4.2: |
Multiscale methods for transport equation / 5.1: |
Governing equations / 5.2.1: |
Adaptive multiscale algorithm for transport equation / 5.2.2: |
The coarse-to-fine grid interpolation operator / 5.2.3: |
Results for a two-dimensional test case / 5.2.4: |
Three-dimensional test cases / 5.2.6: |
Discussion on local boundary conditions / 5.2.7: |
Other approaches for coarsening the transport equation / 5.2.8: |
Applications to Richards' equation / 5.2.9: |
Problem statement / 5.3.1: |
MsFVEM for Richards' equations / 5.3.2: |
Applications to fluid-structure interaction / 5.3.3: |
Multiscale numerical formulation / 5.4.1: |
Numerical examples / 5.4.3: |
Applications of mixed MsFEMs to reservoir modeling and simulation / J. E. Aarnes5.4.4: |
Multiscale method for the three-phase black oil model / 5.5.1: |
Adaptive coarsening of the saturation equations / 5.5.2: |
Utilization of multiscale methods for operational decision support / 5.5.3: |
Multiscale finite volume method for black oil systems / S. H. Lee ; C. Wolfsteiner ; H. A. Tchelepi5.5.4: |
Governing equations and discretized formulation / 5.6.1: |
Multiscale finite volume formulation / 5.6.2: |
Sequential fully implicit coupling and adaptive computation / 5.6.3: |
Remarks / 5.6.4: |
Applications of multiscale finite element methods to stochastic flows in heterogeneous media / 5.7: |
Multiscale methods for stochastic equations / 5.7.1: |
The applications of MsFEMs to uncertainty quantification in inverse problems / 5.7.2: |
Analysis / 5.8: |
Analysis of MsFEMs for linear problems (from Chapter 2) / 6.1: |
Analysis of conforming multiscale finite element methods / 6.1.1: |
Analysis of nonconforming multiscale finite element methods / 6.1.2: |
Analysis of mixed multiscale finite element methods / 6.1.3: |
Analysis of MsFEMs for nonlinear problems (from Chapter 3) / 6.2: |
Analysis of MsFEMs with limited global information (from Chapter 4) / 6.3: |
Mixed finite element methods with limited global information / 6.3.1: |
Glaerkin finite element methods with limited global information / 6.3.2: |
Basic notations / A: |
Review of homogenization / B: |
Linear problems / B.1: |
Special case: One-dimensional problem / B.1.1: |
Multiscale asymptotic expansions / B.1.2: |
Justification of formal expansions / B.1.3: |
Boundary corrections / B.1.4: |
Nonlocal memory effect of homogenization / B.1.5: |
Convection of microstructure / B.1.6: |
Nonlinear problems / B.2: |
References |
Index |
Introduction / 1: |
Challenges and motivation / 1.1: |
Literature review / 1.2: |