Finite Elements 1-2-3
This text is intended for the student who is being introduced for the first time to the Finite Element Method (FEM). Written in a simple, easy to follow manner, the book is a practical guide for learning the basics of the method and applying them to a wide variety of problems. The book focuses on the practical applications of fundamental concepts, with special emphasis on fluid mechanics. Computational experiments are integrated throughout the text via example problems and exercises. A comprehensive finite element instructional computer code, written for the PC using standard FORTRAN 77, is used to support every basic step and solve the set of example problems. The coverage of numerical linear algebra presents a unique numerical scheme based on continuing finite element/finite difference methodologies.
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approximate solution approximation error axisymmetric basis solution boundary condition Code Exercise COLUMN FORMAT computational conﬁrm convection cubic basis deﬁned deﬁnition denotes DIRI Dirichlet boundary conditions discretization Q domain Q element master ENDIF equation error evaluation exact solution ﬁeld ﬁn ﬁnite element algorithm ﬁnite element approximation ﬁnite element basis ﬁnite element method ﬁQ ﬁrst ﬁx ﬁxed ﬂuid FORMO Fortran function Galerkin weak statement geometric global matrix statement hence input ﬁle integral interpolation K N NNODEL REFL Lagrange interpolation LEARN.FE linear basis macro domain master matrix library mesh Q NBUG NEM1 NEM2 NEM3 NNODEL REFL NPR nodal solution nodal values NODE COORDINATES nodes nondimensional NPR NTRAN NAXI NPRI NTRAN NPRN one-dimensional output problem statement procedure quadratic basis quadrilateral recall REFL NPR NTRAN seminorm signiﬁcant source term speciﬁc steady-state Study Problem subroutine thermal conductivity triangle triangular element two-dimensional TYPE K N NNODEL variable verify vertex nodes WRITE(6 yields