Notes on the Finite Element Method
The finite element method (FEM) is widely used to solve boundary value problems to science and engineering. The main advantage of FEM is the facility with which it can be used to solve partial differential equations (PDE) in complex domains As a result it has long been the method of choice to solve problems associated with mechanical engineering. These notes give an overview of the method with applications for Physical Oceanography and Fluid Mechanics. For now only one and two dimensional problems are included.
Professor Randolph Bank, of the UCSD Mathematics Department, has been generous in helping me understand some of the technical difficulties associated with FEM. I am very grateful to him.
Two useful references: Strang, Computationa Science and Engineering and Whiteley, Finite Element Methods: A PracticalGuide, both at UCSD Library
All the latex, Octave/Matlab scripts and fortran codes used for the calculations descrived are freely available on GitHub.
All rights reserved, clinton.winant@gmail.com
Contents
- 1 Equilibrium and Co-oscillating Tides
- 2 Tides in a Two-layer Fluid: Solving a System of Equations
- 3 Time-dependent Waves and Burgers’ Equation
- 4 Two Dimensional Potential Flows
- 5 Two Dimensional Waves on a Rotating Sheet of Water
- 6 Steady Viscous flow
- 7 Non-linear Advection
- 8 The Time-dependent Vorticity Equation: Kelvin-Helmholtz Instability
- 9 Time-dependent Viscous Flows
- 10 Time Dependent Navier Stokes