000			02529 a2200253 4500
008			250124b |||||||| |||| 00| 0 eng d
020			_a9781441919182
082			_a620.0042 ERN
100			_aErn, Alexandre
245			_aTheory and practice of finite elements
260			_aNew York: _bSpringer, _c2004.
300			_axiii, 524p.: _bpbk.: _c24 cm.
440			_aApplied Mathematical Sciences No. 159
504			_aIncludes Bibliographical References and Index
520			_aThe origins of the finite element method can be traced back to the 1950s when engineers started to solve numerically structural mechanics problems in aeronautics. Since then, the field of applications has widened steadily and nowadays encompasses nonlinear solid mechanics, fluid/structure interactions, flows in industrial or geophysical settings, multicomponent reactive turbulent flows, mass transfer in porous media, viscoelastic flows in medical sciences, electromagnetism, wave scattering problems, and option pricing (to cite a few examples). Numerous commercial and academic codes based on the finite element method have been developed over the years. The method has been so successful to solve Partial Differential Equations (PDEs) that the term "Finite Element Method" nowadays refers not only to the mere interpolation technique it is, but also to a fuzzy set of PDEs and approximation techniques. The efficiency of the finite element method relies on two distinct ingredi­ ents: the interpolation capability of finite elements (referred to as the approx­ imability property in this book) and the ability of the user to approximate his model (mostly a set of PDEs) in a proper mathematical setting (thus guar­ anteeing continuity, stability, and consistency properties). Experience shows that failure to produce an approximate solution with an acceptable accuracy is almost invariably linked to departure from the mathematical foundations. Typical examples include non-physical oscillations, spurious modes, and lock­ ing effects. In most cases, a remedy can be designed if the mathematical framework is properly set up. https://link.springer.com/book/10.1007/978-1-4757-4355-5
650			_aMathematical and Computational Engineering
650			_aMathematics and Numerical Analysis
650			_a Partial Differential Equations
650			_aApplications Mathematics in Computer Science
650			_aGalerkin Approximation
650			_aSobolev Space
700			_aGuermond, Jean-Luc _eCo-author
942			_cTD _2ddc
999			_c61582 _d61582