Location and Time: 8:00-8:50 MWF in Eng. E103
Instructor: K.M. McArthur
Office, phone, and email: Weber 110, 1-6739, mcarthur@math.colostate.edu
Office Hrs: To be determined and by appointment.
Description: Finite element methods arose as a technique for solving structural engineering problems. They are now recognized as a general numerical method for solving differential and integral equations. The use of finite element methods is now so common that software packages exist for many areas of application. More recently they are being used as preconditioning tools for spectral methods applied to problems such as in atmospheric science.
Prerequisites: Some knowledge of basic PDEs(extensively covered in M332 or M532 or M545), of linear algebra (M560), of some analysis(dealing with multivariable calculus), and of Matlab, C, C++, or possible others.
Tentative Text: K. Ericksson, D. Estep, P. Hansbo, and C. Johnson, Computational Differential Equations, Cambridge University Press, 1996. The first five chapters of this book should be review and so will not be covered. Chapter 6, which defines Galerkin's Method, will be covered quickly. Chapter 7, which covers linear algebra, will not be covered since M560 is a prerequisite. The material in Part II, chapters 8 through 12 will take approximately 5 weeks, and about 70 percent of the material in Part III, chapters 13 through 21, will be covered in 7 to 8 weeks. Along the way, we may examine DEs and PDEs with domains and/or boundary conditions that lead to difficulties whose solutions may require extending the concepts covered in M560.