Numerical solutions of 2- dimensional partial differential equations with B-spline finite element methods

This Ph.D. thesis consists of five chapters. In the first chapter, after giving some generalinformation about the fundamental concepts and 2?dimensional partial differential equations usedin the thesis, fundamental concepts about the finite difference, variational and finite elementmethods together with spline and B-spline functions are presented.The second, third, fourth and fifth chapters of the thesis make up its original parts. In thesecond chapter, 2?dimensional cubic, quintic and septic B-spline bases functions which will beused in the solution of 2?dimensional partial differential equations are modified.In the third chapter, numerical solutions of time-independent 2?dimensional Poisson equationgiven with boundary conditions are obtained with Galerkin finite element method by using variousdegrees of B-spline functions. The obtained numerical results are compared with existingresults in the literature, and they are given with their error norms L2 and L? in the form of tables.In the fourth chapter, 2?dimensional diffusion equation given with initial and boundary conditionsis solved by using Galerkin finite element method with various degrees of B-spline functions. Theobtained numerical results are compared with existing results in the literature, and they are givenwith their error norms L2 and L? in the form of tables.In the fifth chapter, 2?dimensional unsteady Burgers equation given with initialand boundary conditions is solved by using Galerkin finite element method with various degrees ofB-spline functions. The obtained numerical results are compared with existing results in theliterature, and they are given with their error norms L2 and L? in the form of tables.