Syllabus
The course provides an overview about the proof techniques of existence and uniqueness of solutions of nonlinear partial differential equations and about their solution by the finite element method. We will use the method of monotone operators, potential operators, and we will consider questions of the existence and uniqueness of the solution, discretization by the finite element method and convergence of this method.
We will use various mathematical terms such as Banach spaces, weak convergence, and monotone operators for numerical solution of particular nonlinear problems of electro-engineering. We will approximate models of heat radiation and distribution of electric, magnetic, and temperature fields in rotating electric machines and transformers by the finite element method.
The emphasis will be put on questions of existence and uniqueness of both the continuous and discrete solutions, and on questions of convergence and algorithms.
Annotation
The course aims at the computation of the nonlinear stationary magnetic field, stationary problem of heat radiation, nonlinear and anisotropic heat conduction, nonstationary problem of heat conduction and on the time periodic
Maxwell equations. We will study the existence and uniqueness of the solution and discretization by the finite element method.