The Study Of Error Estimations And Finite Element Methods For Engineering Mechanics

This dissertation evolves from a set of my previous papers published and to be published. Its contents include results on the finite element method for the dynamics equations, the lumped mass finite element methods and error estimations for solving the parabolic problem , fourth order nonstationary elliptic equation, the nonstationary Stokes problem and Bingham fluid problem, the finite element methods and error estimations for solving linear and nonlinear the hyperbolic equations. There are six chapters in the dissertation. Chapter 1 presents developments of the finite element. Chapter 2 formulates the lumped mass finite element methods and error estimations for parabolic problem. Chapter 3 deals with the lumped mass finite element methods and error estimations for fourth order nonstationary elliptic equation. Chapter 4 disscusses finite element methods and error estimations for linear and nonlinear the hyperbolic equations. Chapter 5 presents the lumped mass finite element methods and error estimations for the nonstationary Stokes problem. Chapter 6 deals with the lumped mass finite element methods and error estimations for Bingham fluid problem.