Titlebook: Computational Engineering - Introduction to Numerical Methods; Michael Schäfer Book 2022Latest edition The Editor(s) (if applicable) and T

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Finite-Volume Methods,Finite-volume methods (FVM)—sometimes also called box methods—are mainly employed for the numerical solution of problems in fluid mechanics, where they were introduced in the 1970s by McDonald, MacCormack, and Paullay. However, the application of the FVM is not limited to flow problems.

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Finite-Element Methods,The techniques known today as finite-element methods (FEM) date back to work conducted between 1940 and 1960 in the field of structural mechanics. The term finite element was introduced by Clough (1960). Nowadays, the FEM is widely used primarily for numerical computations in solid mechanics and can be regarded as a standard tool there.

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,Solution of Algebraic Systems of Equations,The discretization of steady or unsteady problems with implicit time integration, either by finite-volume or finite-element methods, results in large sparse systems of algebraic equations. The solution procedure for these equation systems is an important part of a numerical method.

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