The Finite Element Method for Partial Differential Equations

• Apply the basic principles for deriving weak formulations of linear PDEs.
• Compute local and global finite element matrices.
• Efficiently setup and solve systems of linear algebraic equation resulting from FEM discretizations in Matlab.
• Assess the accuracy of computed approximate solutions.
• Utilize graded and unstructured meshes for use with FEM in 1D and 2D and understand their pros and cons.
• Implement computer programs to solve BVPs using FEM in 1D and 2D.
• Knowledge of basic direct and iterative methods for solving systems of algebraic equations in Matlab.
• Independently solve a special topics problem offered in the course.
• Written and oral presentation of results in reports and a poster

The Finite Element Method (FEM) is of major importance for computer-based simulation for engineering analysis, insight and decision support. In this course we give a concise treatment of the various aspects of the Finite Element Method (FEM) including: local and global interpolation functions based on triangular elements, boundary value problems for partial differential equations, the assembly of global algebraic system of equations, Gaussian elimination for banded systems, iterative solution methods, time-dependent problems. Systematic development, through exercises, of computer software implementing the FEM, and possible exploitation of high-performance computing. The final assignment of the course will be in one of the special topics, for example an application of the finite element method for the solution of a particular problem from engineering sciences. Throughout the course, emphasis is on learning methods behind FEM, and linking theory and application.

02002/02631/02632/02633/02601/02603, Basic course in programming with Matlab.
Basic course in numerical algorithms.

Three weeks of practical computer exercises.

This course together with 02686 and 02687 forms a basis for understanding and applying numerical methods for the solution of differential equations. Course 02689 supplements these course with details on modern scientific calculations methods.