Finite Element Methods
Galerkin formulation, mixed methods, and a-posteriori error estimation.
Finite Element Methods. Galerkin formulation, mixed methods, and a-posteriori error estimation.
Foundations and canonical references
The standard treatments of finite element methods approach the subject from complementary angles. Brenner, The Mathematical Theory of Finite Element Methods (2008) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Zienkiewicz, The Finite Element Method: Its Basis and Fundamentals (2013) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for finite element 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 · 2008The Mathematical Theory of Finite Element Methodsbrenner-2008, scott-2008
- textbook · primary · 2013The Finite Element Method: Its Basis and Fundamentalszienkiewicz-2013, taylor-robert-2013, zhu-2013
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