Finite element method: Difference between revisions

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In the 1990s FEM was proposed for use in stochastic modeling for numerically solving probability models<ref>{{cite journal |title=Methods with high accuracy for finite element probability computing |author1=Peng Long |author2=Wang Jinliang |author3=Zhu Qiding |journal=Journal of Computational and Applied Mathematics |volume=59 |issue=2 |date=19 May 1995 |pages=181–189 |doi=10.1016/0377-0427(94)00027-X |doi-access= }}</ref> and later for reliability assessment.<ref>{{cite book |first1=Achintya |last1=Haldar |first2=Sankaran |last2=Mahadevan |title=Reliability Assessment Using Stochastic Finite Element Analysis |publisher=John Wiley & Sons |isbn=978-0471369615 |year=2000}}</ref>

FEM is widely applied for approximating differential equations that describe physical systems. This method is very popular in the community of [[Computational fluid dynamics]], and there are many applications for solving [[Navier–Stokes equations]] with FEM.<ref>{{cite book |last1=Girault |first1=Vivette |last2=Raviart |first2=Pierre-Arnaud |title=Finite Element Approximation of the Navier-Stokes Equations |volume=749 |year=1979 |publisher=Springer Berlin|isbn=978-3-540-09557-6}}</ref><ref>{{cite book |last1=Cuvelier |first1=Cornelis |last2=Segal |first2=August |last3=Van Steenhoven |first3=Anton A |title=Finite Element Methods and Navier-Stokes Equations |volume=22 |year=1986 |publisher=Springer Science & Business Media|isbn=978-1-4020-0309-7}}</ref><ref>{{cite book |last1=Girault |first1=Vivette |last2=Raviart |first2=Pierre-Arnaud |title=Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms |volume=5 |year=2012 |publisher=Springer Science & Business Media|isbn=978-3-642-64888-5}}</ref> Recently, the application of FEM has been increasing in the researches of computational plasma. Promising numerical results using FEM for [[Magnetohydrodynamics]], [[Vlasov equation]], and [[Schrödinger equation]] have been proposed.<ref>{{cite journal |last1=Karakashian |first1=Ohannes |last2=Makridakis |first2=Charalambos |year=1999 |title=A Space-Time Finite Element Method for the Nonlinear Schrödinger Equation: The Continuous Galerkin Method |journal=SIAM Journal on Numerical Analysis |publisher=SIAM |volume=36 |issue=6 |pages=1779–1807 |doi=10.10161137/0377-0427(94)00027-XS0036142997330111 |doi-access= |year=1999 |publisher=SIAM}}</ref><ref>{{cite journal |last1=Sovinec |first1=Carl R. |last2=Glasser |first2=A.H. |last3=Gianakon |first3=T.A. |last4=Barnes |first4=D.C. |last5=Nebel |first5=R.A. |last6=Kruger |first6=S.E. |last7=Schnack |first7=D.D. |last8=Plimpton |first8=S.J. |last9=Tarditi |first9=A. |last10=Chu |first10=M.S. |title=Nonlinear Magnetohydrodynamics Simulation Using High-Order Finite Elements |journal=Journal of Computational Physics |volume=195 |issue=1 |pages=355–386 |year=2004 |doi=10.1016/j.jcp.2003.10.004 |publisher=Elsevier|bibcode=2004JCoPh.195..355S }}</ref>

==See also==