The finite-element method for solving conservation equations in glaciology

Dr James L. Fastook

Abstract:

• Contents
• Introduction
• Conservation equations
• Finite-element Formulation
  • Weak Variational Formulation
  • Galerkin Approximation
  • Basis and Shape Functions
  • Extension to 2- and 3-Dimensions
  • Time-dependent Solution
• Mass Conservation
  • The Continuity Equation
  • The Finite Element Method
    • Construction of the Variational Statement of the Problem
    • Generation of a Grid and Basis Functions
    • Construction of the Algebraic System of Equations
  • Mass Balance
  • Coordinate System
• Momentum Conservation
  • Basic equations: General non-Newtonian fluid flow (incompressible)
  • Alternate derivation: Extension to 3-D
    • Penalty Method for eliminating pressures
• Energy Conservation
  • Semi-analytic steady state temperature solution with vertical velocity
  • One-Dimensional Temperature Model, with advection, and column-integrated velocities
  • Flow law constant, dependence on temperature
  • Basal Boundary Conditions
• Conclusion
• Acknowledgments
• Tables
• References
• About this document ...