Discussion Overview
The discussion centers on finding introductory textbooks for solving partial differential equations (PDEs) using finite element methods (FEM), with a particular interest in applications to fluid flow problems. Participants share recommendations and express their preferences for different numerical methods.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
Main Points Raised
- One participant seeks recommendations for beginner-level textbooks on FEM for PDEs, specifically for fluid flow applications.
- Another participant suggests considering finite volume methods for fluid flow instead of FEM.
- A different participant expresses a preference for FEM over finite volume methods, citing their research needs in rotating flows and a dislike for commercial CFD packages.
- Several participants recommend the book "Spectral/hp methods for computational fluid dynamics" by Karniadakis and Sherwin, noting its practical approach and various features.
- Classic texts by Zienkiewicz & Taylor and Strang & Fix are mentioned, though their current relevance is questioned.
- A suggestion is made to refer to a paper on implementing FEM in MATLAB, highlighting a practical resource for immediate application.
- One participant challenges the reasoning behind choosing to program a custom FEM, suggesting that a commercial finite volume solver might be more efficient for research purposes.
Areas of Agreement / Disagreement
Participants express differing views on the suitability of finite element methods versus finite volume methods for fluid flow problems. There is no consensus on the best approach, as some advocate for FEM while others recommend finite volume methods.
Contextual Notes
Participants' preferences are influenced by their individual experiences and research requirements, leading to a variety of perspectives on the choice of numerical methods. The discussion reflects a range of assumptions about the capabilities and limitations of FEM and finite volume methods.