Finite element method

The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. Studying or analyzing a phenomenon with FEM is often referred to as finite element analysis (FEA).

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Alt: enExample of 2D mesh; enFEM_example_of_2D_solution; enSixteen triangular basis functions used to reconstruct J0; enSummation of basis functions
Caption: enFEM mesh created by an analyst prior to finding a solution to a magnetic problem using FEM software. Colors indicate that the analyst has set material properties for each zone, in this case, a conducting wire coil in orange; a ferromagnetic component in light blue; and air in grey. Although the geometry may seem simple, it would be very challenging to calculate the magnetic field for this setup without FEM software, using equations alone.; enFEM solution to the problem at left, involving a cylindrically shaped magnetic shield. The ferromagnetic cylindrical part is shielding the area inside the cylinder by diverting the magnetic field created by the coil . The color represents the amplitude of the magnetic flux density, as indicated by the scale in the inset legend, red being high amplitude. The area inside the cylinder is the low amplitude , which suggests that the shield is performing as it was designed to.; enThe linear combination of basis functions reproduces J0 to any desired accuracy.; 16
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Comment: enThe finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. Studying or analyzing a phenomenon with FEM is often referred to as finite element analysis (FEA).
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Has abstract: enThe finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points. The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates the unknown function over the domain.The simple equations that model these finite elements are then assembled into a larger system of equations that models the entire problem. The FEM then approximates a solution by minimizing an associated error function via the calculus of variations. Studying or analyzing a phenomenon with FEM is often referred to as finite element analysis (FEA).
Header: enInterpolation of a Bessel function
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Hypernym: Technique
Image: enExample of 2D mesh.png; enFEM_example_of_2D_solution.png; enLinear interpolation of J0 .svg; enLinear interpolation of J1 .svg
Is primary topic of: Finite element method
Label: enFinite element method
Link from a Wikipage to an external page: link.springer.com/book/10.1007/978-3-319-70428-9; books.google.com/books%3Fid=HIwSDAAAQBAJ&printsec=frontcover%23v=onepage&q=%22finite%20element%22&f=false; books.google.com/books%3Fid=YocoaH8lnx8C&printsec=frontcover%23v=onepage&q&f=false; people.maths.ox.ac.uk/suli/fem.pdf
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SameAs: 25w4x; 4017233-8; Anàlisi d'elements finits; Baigtinių elementų metodas; Eindige-elementenmethode; Elementtimenetelmä; Elementu finituen metodo; Finita elementmetoden; Finite-Elemente-Methode; Finite element method; Finite element method; Finittelementmetoden; Lõplike elementide meetod; m.03110; Méthode des éléments finis; Metoda elementów skończonych; Metoda končnih elementov; Metóda konečných prvkov; Metoda konečných prvků; Metode elemen hingga; Metodo degli elementi finiti; Método de los elementos finitos; Método dos elementos finitos; Phương pháp phần tử hữu hạn; Q220184; Sonlu elemanlar yöntemi; Sonlu elementlər üsulu; Végeselemes módszer; Μέθοδος πεπερασμένων στοιχείων; Метод конечных элементов; Метод на крайните елементи; Метод скінченних елементів; אלמנטים סופיים; روش اجزاء محدود; طريقة العناصر المنتهية; परिमित अवयव विधि; ระเบียบวิธีไฟไนต์เอลิเมนต์; 有限元素法; 有限要素法; 유한요소법
Subject: Category:Canadian inventions; Category:Computational electromagnetics; Category:Continuum mechanics; Category:Finite element method; Category:Numerical differential equations; Category:Partial differential equations; Category:Russian inventions; Category:Structural analysis
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Finite element method

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