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Contents
Contents
Lectures on the Finite Element Method
Dongwoo Sheen
School of Mathematics, Seoul National University, Seoul 151-747
Date:
April 9, 2001
Contents
Main Model Problems
Navier-Stokes System
Boundary conditions
Navier-Stokes equations (Incompressible fluid)
Incompressible, homogeneous Navier-Stokes equations
Linearized Navier-Stokes equations (Stokes equations)
Euler's equations (perfect fluid)
Boundary conditions
Linear Elasticity
Isotropic case
Homogeneous isotropic case
Heat equation
Introduction to FEM for Elliptic Problems
Variational formulation of a one-dimensional model problem
Basic ideas of Several Numerical Methods
Finite Difference Methods
Finite Element Methods
Collocation Method
The Least Square Method
Error Estimate for FEM
Sobolev Spaces
Distributions
Multi-index and partial derivatives
Definition of Distribution
Examples of distribution
Differentiation of distribution
Sobolev Spaces
Prolongation
Trace Theorem
Application of Trace Theorem
Application to finite element subspace of
Compactness results
The Sobolev Space
About this document ...
Numerical Linear Algebra 2001-04-27
