Application of finite element methods for some nonlinear partial differential equations

The thesis is consists of five sections. In the first section, the basic information about Burger and Rlw equations which will be used during the work is given. Then, the solution techniques which will be used for solving the equations are introduced. In the second section, Burgers' equation is obtained using the methods of cubic B-spline collocation and quadratic B-spline Galerkin. The finite element methods are constructed within the quadratic and cubic B-splines as an approximate function, respectively, over this mesh. In the third section, the Rlw equation is solved by a Petrov-Galerkin method using quadratic B-spline finite elements. The motion of solitary waves is studied to assess the properties of the algorithm. In the fourth section, The solutions of single perturbation problems will be done. Collocation method is applied with quadratic and cubic B-spline base function over the geometrically graded mesh of the solution domain. In the fifth section, Quadratic B-spline collocation and Cubic B-spline collocation methods will be applied to find the numeric solutions of Burger equation. The results of both schemes are compared with some test problems. Keywords: Cybernetics, Collocation, Finite elements, Graded mesh, Hydrodynamics, Numerical analysis, Petrov-Galerkin, RLW equation, Spline