Syllabus
Nonlinear differential equations in divergence form.
Caratheodory growth condition, Nemycky operators.
Variational methods and aplication of theory of monotone and potential operator, proof of existence of solution.
Numerical solution of nonlinear diferential equation by abstract numerical method.
Existence of solution, stability, consistency, convergence of abstract numerical method.
Application on conforming finite element method and discontinuous Galerkin method.
Annotation
Nonlinear differential equations in divergence form.
Carathéodory grow condition, Nemycki operator.
Variational methods and applications of theory of monotone a potential operators.
Numerical solution of nonlinear differential equations by abstract numerical methods.
Existence of the solution, stability, consistency and convergence of abstract numerical methods.