Contains a thorough derivation of the finite element equations as well as sections on programming the necessary calculations, solving the finite element equations, and using a posteriori error estimates to produce validated solutions. Practical in nature, the book includes a carefully documented collection of MATLAB programs implementing the ideas presented.
Contains a thorough derivation of the finite element equations as well as sections on programming the necessary calculations, solving the finite element equations, and using a posteriori error estimates to produce validated solutions. Practical in nature, the book includes a carefully documented collection of MATLAB programs implementing the ideas presented.
Mark S. Gockenbach is a Professor of Mathematical Sciences at Michigan Technological University. His research interests include inverse problems, computational optimization, and mathematical software. His first book, Partial Differential Equations: Analytical and Numerical Methods, was published by SIAM in 2002.
Inhaltsangabe
Preface; Part I. The Basic Framework for Stationary Problems: 1. Some model PDEs; 2. The weak form of a BVP; 3. The Galerkin method; 4. Piecewise polynomials and the finite element method; 5. Convergence of the finite element method; Part II. Data Structures and Implementation: 6. The mesh data structure; 7. Programming the finite element method: Linear Lagrange triangles; 8. Lagrange triangles of arbitrary degree; 9. The finite element method for general BVPs; Part III. Solving the Finite Element Equations: 10. Direct solution of sparse linear systems; 11. Iterative methods: Conjugate gradients; 12. The classical stationary iterations; 13. The multigrid method; Part IV. Adaptive Methods: 14. Adaptive mesh generation; 15. Error estimators and indicators; Bibliography; Index.
Preface; Part I. The Basic Framework for Stationary Problems: 1. Some model PDEs; 2. The weak form of a BVP; 3. The Galerkin method; 4. Piecewise polynomials and the finite element method; 5. Convergence of the finite element method; Part II. Data Structures and Implementation: 6. The mesh data structure; 7. Programming the finite element method: Linear Lagrange triangles; 8. Lagrange triangles of arbitrary degree; 9. The finite element method for general BVPs; Part III. Solving the Finite Element Equations: 10. Direct solution of sparse linear systems; 11. Iterative methods: Conjugate gradients; 12. The classical stationary iterations; 13. The multigrid method; Part IV. Adaptive Methods: 14. Adaptive mesh generation; 15. Error estimators and indicators; Bibliography; Index.
Rezensionen
'Upon completion of this book a student or researcher would be well prepared to employ finite elements for an application problem or proceed to the cutting edge of research in finite element methods. The accuracy and the thoroughness of the book are excellent.' Anthony Kearsley, National Institute of Standards and Technology
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