An Introduction to the Mathematical Theory of Finite Elements
E483186
An Introduction to the Mathematical Theory of Finite Elements is a foundational textbook that rigorously develops the mathematical underpinnings of the finite element method used in numerical analysis and engineering.
All labels observed (2)
| Label | Occurrences |
|---|---|
| An Introduction to the Mathematical Theory of Finite Elements canonical | 1 |
| The Mathematical Theory of Finite Element Methods | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4966481 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: An Introduction to the Mathematical Theory of Finite Elements Context triple: [J. Tinsley Oden, notableWork, An Introduction to the Mathematical Theory of Finite Elements]
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A.
Finite Element Methods for Flow Problems
"Finite Element Methods for Flow Problems" is a foundational textbook that develops and applies finite element techniques to the numerical simulation of fluid flow and related transport phenomena.
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B.
The Finite Element Method: Linear Static and Dynamic Finite Element Analysis
The Finite Element Method: Linear Static and Dynamic Finite Element Analysis is a foundational textbook that rigorously presents the theory and application of finite element techniques for solving linear static and dynamic problems in engineering and applied sciences.
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C.
Methods of Mathematical Physics
Methods of Mathematical Physics is a classic two-volume textbook by Richard Courant and David Hilbert that rigorously develops the mathematical foundations and techniques used in theoretical physics.
-
D.
finite element method
The finite element method is a numerical technique for solving complex engineering and physical problems by approximating solutions over discretized domains, widely used in structural analysis, heat transfer, fluid dynamics, and related fields.
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E.
Lectures on Cauchy’s problem in linear partial differential equations
"Lectures on Cauchy’s Problem in Linear Partial Differential Equations" is a classic mathematical treatise by Jacques Hadamard that systematically develops the theory of existence, uniqueness, and well-posedness for solutions to linear partial differential equations.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: An Introduction to the Mathematical Theory of Finite Elements Target entity description: An Introduction to the Mathematical Theory of Finite Elements is a foundational textbook that rigorously develops the mathematical underpinnings of the finite element method used in numerical analysis and engineering.
-
A.
Finite Element Methods for Flow Problems
"Finite Element Methods for Flow Problems" is a foundational textbook that develops and applies finite element techniques to the numerical simulation of fluid flow and related transport phenomena.
-
B.
The Finite Element Method: Linear Static and Dynamic Finite Element Analysis
The Finite Element Method: Linear Static and Dynamic Finite Element Analysis is a foundational textbook that rigorously presents the theory and application of finite element techniques for solving linear static and dynamic problems in engineering and applied sciences.
-
C.
Methods of Mathematical Physics
Methods of Mathematical Physics is a classic two-volume textbook by Richard Courant and David Hilbert that rigorously develops the mathematical foundations and techniques used in theoretical physics.
-
D.
finite element method
The finite element method is a numerical technique for solving complex engineering and physical problems by approximating solutions over discretized domains, widely used in structural analysis, heat transfer, fluid dynamics, and related fields.
-
E.
Lectures on Cauchy’s problem in linear partial differential equations
"Lectures on Cauchy’s Problem in Linear Partial Differential Equations" is a classic mathematical treatise by Jacques Hadamard that systematically develops the theory of existence, uniqueness, and well-posedness for solutions to linear partial differential equations.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematics textbook ⓘ numerical analysis textbook ⓘ textbook ⓘ |
| approach | rigorous mathematical treatment of finite element method ⓘ |
| audience |
graduate students in engineering
ⓘ
graduate students in mathematics ⓘ researchers in numerical analysis ⓘ |
| author |
L. Ridgway Scott
ⓘ
Susanne C. Brenner ⓘ |
| field |
applied mathematics
ⓘ
finite element method ⓘ numerical analysis ⓘ partial differential equations ⓘ |
| focus | mathematical foundations of finite element method ⓘ |
| goal |
to develop rigorous error estimates for finite element approximations
ⓘ
to present a unified framework for finite element analysis ⓘ |
| language | English ⓘ |
| methodology |
functional analysis techniques
ⓘ
variational methods ⓘ |
| relatedTo |
computational mechanics
ⓘ
engineering analysis ⓘ scientific computing ⓘ |
| topic |
Céa’s lemma
ⓘ
Galerkin method ⓘ Lax–Milgram theorem applications ⓘ Sobolev spaces ⓘ a priori error analysis ⓘ adaptive finite element methods ⓘ approximation theory ⓘ elliptic boundary value problems ⓘ error estimates ⓘ finite element implementation issues ⓘ finite element spaces ⓘ interpolation estimates ⓘ mixed finite element methods ⓘ nonconforming finite elements ⓘ stability analysis ⓘ variational formulation of boundary value problems ⓘ |
| use |
graduate-level teaching
ⓘ
reference for researchers ⓘ self-study ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: An Introduction to the Mathematical Theory of Finite Elements Description of subject: An Introduction to the Mathematical Theory of Finite Elements is a foundational textbook that rigorously develops the mathematical underpinnings of the finite element method used in numerical analysis and engineering.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: An Introduction to the Mathematical Theory of Finite Elements