FINITE ELEMENT METHOD AND ITS APPLICATIONS discusses the methods in a general frame and the performance on the computer, the variational formulations for elliptic boundary value problems, the error estimates and convergence for finite element approximate solutions and nonstandard finite element. In particular, presentations of the subject include the applications of finite element method to various scientific and engineering problems, for example, three dimensional elastic beam, elastic mechanics, three dimensional neutron diffusion problems, magneto hydrodynamics, three dimensional turbomachinery flows, Navier-Stokes equations and bifurcation phenomena for nonlinear problem, etc. Most applications results were established by the authors in the past three decades.

The Structure of Finite Element Method / Elements and Shape functions / Procedure and Performance of Computation of Finite Element Method / Sobolev Space / The Variational Principle for Elliptic Boundary Value Problem and Error Estimate of Finite Element Approximation Solution / Nonstandard Finite Element Methods / Applications of Finite Element Method in the Engineering / Finite Element Analysis for Internal Flow in Turbomachine / Finite Element Approximation for the Navier-Stokes equations / References.

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