Author | Mรผller, Siegfried. author |
---|---|
Title | Adaptive Multiscale Schemes for Conservation Laws [electronic resource] / by Siegfried Mรผller |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2003 |
Connect to | http://dx.doi.org/10.1007/978-3-642-18164-1 |
Descript | XIV, 188 p. 1 illus. online resource |
1 Model Problem and Its Discretization -- 1.1 Conservation Laws -- 1.2 Finite Volume Methods -- 2 Multiscale Setting -- 2.1 Hierarchy of Meshes -- 2.2 Motivation -- 2.3 Box Wavelet -- 2.4 Change of Stable Completion -- 2.5 Box Wavelet with Higher Vanishing Moments -- 2.6 Multiscale Transformation -- 3 Locally Refined Spaces -- 3.1 Adaptive Grid and Significant Details -- 3.2 Grading -- 3.3 Local Multiscale Transformation -- 3.4 Grading Parameter -- 3.5 Locally Uniform Grids -- 3.6 Algorithms: Encoding, Thresholding, Grading, Decoding -- 3.7 Conservation Property -- 3.8 Application to Curvilinear Grids -- 4 Adaptive Finite Volume Scheme -- 4.1 Construction -- 4.2 A gorithms: Initial data, Prediction, Fluxes and Evolution -- 5 Error Analysis -- 5.1 Perturbation Error -- 5.2 Stability of Approximation -- 5.3 Reliability of Prediction -- 6 Data Structures and Memory Management -- 6.1 Algorithmic Requirements and Design Criteria -- 6.2 Hashing -- 6.3 Data Structures -- 7 Numerical Experiments -- 7.1 Parameter Studies -- 7.2 Real World Application -- A Plots of Numerical Experiments -- B The Context of Biorthogonal Wavelets -- B.1 General Setting -- B.1.1 Multiscale Basis -- B.1.2 Stable Completion -- B.1.3 Multiscale Transformation -- B.2 Biorthogonal Wavelets of the Box Function -- B.2.1 Haar Wavelets -- B.2.2 Biorthogonal Wavelets on the Real Line -- References -- List of Figures -- List of Tables -- Notation