Lecture notes for CS 455: Numerical Methods for PDEs

Lectures:

• Class Introduction: (handout)
• Intro PDEs: (handout - full - four up)
• M&M 1: (handout - full - four up)
• M&M 2: (handout - full - four up)
• M&M 3: (handout - full - four up)
• M&M 4: (handout - full - four up)
• M&M 5: (handout - full - four up)
• M&M 6: (handout - full - four up)

• A&B 1: (handout - full - four up)
• A&B 2: (handout - full - four up)
• A&B 3: (handout - full - four up)
• A&B 4: (handout - full - four up)

Finite Element lectures based on Eriksson, Estep, Hansbo, and Johnson, Computational Differential Equations, Cambridge University Press.

• EEH&J 1: (handout - full - four up)
• EEH&J 2: (handout - full - four up)
• EEH&J 3: (handout - full - four up)
• EEH&J 4: (handout - full - four up)
• EEH&J 5: (handout - full - four up)
• EEH&J 6: (handout - full - four up)
• EEH&J 7: (handout - full - four up)

Apart from the required text books the following books are useful.

Numerical Solution of PDEs

• K. Eriksson e.a., Computational Differential Equations, Cambridge
• H. P. Langtangen, Computational Partial Differential Equations, Springer
• Ph. G. Ciarlet, The Finite Element Method for Elliptic Problems, SIAM
• Ainsworth & Oden, A Posteriori Error Estimation in Finite Element Analysis, Wiley InterScience
• Babuska & Strouboulis, The Finite Element Method and its Reliability, Oxford

PDEs and Applied Mathematics

• Lanczos, The Variational Principles of Mechanics, Dover
• V. A. Arnold, Mathematical Methods of Classical Mechanics, Springer
• E. Zauderer, Partial Differential Equations, Wiley
• C. C. Lin & L. A. Segel, Mathematics Applied to Deterministic Problems in the Natural Sciences, SIAM

Basics

• E. Kreyszig, Advanced Engineering Mathematics, Wiley
• L. N. Trefethen & Bau, Numerical Linear Algebra, SIAM
• G. H. Golub and C. Van Loan, Matrix Computations, John Hopkins University Press

General Numerical Analysis

• M. T. Heath, Scientific Computing: An Introductory Survey 2^nd edition, McGrawHill
• A. Quarteroni e.a, Numerical Mathematics, Springer

Solving Linear Systems and Eigenvalue Problems

• G. Meurant, Computer Solution of Large Linear Systems, North Holland
• Duff, Dongarra, Sorensen, and Van der Vorst, Numerical Linear Algebra for High Performance Computers, SIAM
• A. Greenbaum, Iterative Methods for Solving Linear Systems, SIAM
• Y. Saad, Iterative Methods for Sparse Linear Systems, ITP
• U. Trottenberg, C. W. Oosterlee, and A. Schueller, Multigrid, Academic Press