Finite Volume and Finite Difference Methods
Conservation-law discretizations and structured-grid solvers.
Finite Volume and Finite Difference Methods. Conservation-law discretizations and structured-grid solvers.
Foundations and canonical references
The standard treatments of finite volume and finite difference methods approach the subject from complementary angles. Leveque, Finite Volume Methods for Hyperbolic Problems (2002) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Leveque, Finite Difference Methods for Ordinary and Partial Differential Equations (2007) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for finite volume and finite difference methods include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2002Finite Volume Methods for Hyperbolic Problemsleveque-2002
- textbook · primary · 2007Finite Difference Methods for Ordinary and Partial Differential Equationsleveque-2007
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