The Finite Volume, Finite Difference, and Finite Elements Methods as Numerical Methods for Physical Field Problems

I. Introduction II. Foundations A. The Mathematical Structure of Physical Field Theories B. Geometric Objects and Orientation 1. Space-Time Objects C. Physical Laws and Physical Quantities 1. Local and Global Quantities 2. Equations D. Classification of Physical Quantities 1. Space-Time Viewpoint E. Topological Laws F. Constitutive Relations 1. Constitutive Equations and Discretization Error G. Boundary Conditions and Sources H. The Scope of the Structural Approach III. Representations A. Geometry 1. Cell Complexes 2. Primary and Secondary Mesh 3. Incidence Numbers 4. Chains 5. The Boundary of a Chain B. Fields 1. Cochains 2. Limit Systems C. Topological Laws 1. The Coboundary Operator 2. Properties of the Coboundary Operator 3...

• Type: Journal
• Year: 2000
• Where: Advances in Imaging and Electron Physics
• Authors: Claudio Mattiussi
• Keywords: Electromagnetism-like Algorithm, Finite Difference Method, Finite Difference Time Domain, Finite Element Method, Finite Volume Methods, Numerical Methods