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Generalizations of the Finite Element Method
Open Mathematics, 2012 Abstract This paper is concerned with the generalization of the finite element method via the use of non-polynomial enrichment functions. Several methods employ this general approach, e.g. the extended finite element method and the generalized finite element method.
Schweitzer Marc
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An Analysis of the Finite Element Method [PDF]
Journal of Applied Mechanics, 1974 G. Strang, G. Fix, D. Griffin
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Can physics-informed neural networks beat the finite element method? [PDF]
IMA Journal of Applied Mathematics, 2023 Partial differential equations (PDEs) play a fundamental role in the mathematical modelling of many processes and systems in physical, biological and other sciences.
T. G. Grossmann +3 more
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The extended/generalized finite element method: An overview of the method and its applications
International Journal for Numerical Methods in Engineering, 2010 T. Fries, T. Belytschko
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Eighty Years of the Finite Element Method: Birth, Evolution, and Future [PDF]
Archives of Computational Methods in Engineering, 2021 This document presents comprehensive historical accounts on the developments of finite element methods (FEM) since 1941, with a specific emphasis on developments related to solid mechanics.
Wing Kam Liu, Shaofan Li, Harold S. Park
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A finite element method for electrowetting on dielectric [PDF]
Journal of Computational Physics, 2021 We consider the problem of electrowetting on dielectric (EWoD). The system involves the dynamics of a conducting droplet, which is immersed in another dielectric fluid, on a dielectric substrate under an applied voltage. The fluid dynamics is modeled by the two-phase incompressible Navier-Stokes equations with the standard interface conditions, the ...
Quan Zhao, Weiqing Ren
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J, 2023 This study aims to improve the computational efficiency of the frequency domain analysis of medium-frequency transformers (MFTs) with the presence of large clearance distances and fine foil windings.
Siamak Pourkeivannour +4 more
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Advanced Engineering Research, 2023 Introduction. When numerically solving problems of elasticity theory in a three-dimensional formulation by the finite element method, finite elements (FE) in the form of parallelepipeds, prisms and tetrahedra are used.
P. P. Gaidzhurov, N. A. Saveleva
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Crack Propagation by Finite Element Method [PDF]
Fracture and Structural Integrity, 2018 Crack propagation simulation began with the development of the finite element method; the analyses were conducted to obtain a basic understanding of the crack growth.
Luiz Carlos H. Ricardo
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The vortex method with finite elements [PDF]
Mathematics of Computation, 1981 This work shows that the method of charcteristics is well suited for the numerical solution of first order hyperbolic partial differential equations whose coefficients are approximated by functions piecewise constant on a finite element triangulation of the domain of integration.
Bardos, Claude +2 more
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