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This book is aimed at senior undergraduates, graduates and engineers. It fills the gap between the numerous textbooks on traditional Applied Mechanics and postgraduate books on Finite Element Methods.Fills the gap between the applied mechanics and finite element methodsDiscusses basic structural concepts and energy theorems, the discrete system, in-plane quadrilateral elements, field problems and mathematical modelling, among other topicsAimed at senior undergraduates, graduates and engineers

Finite element method. --- Engineering mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis --- Mathematics

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This is the first book devoted to the least-squares finite element method (LSFEM), which is a simple, efficient and robust technique for the numerical solution of partial differential equations. The book demonstrates that the LSFEM can solve a broad range of problems in fluid dynamics and electromagnetics with only one mathematical/computational formulation. The book shows that commonly adopted special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal-order elements, operator splitting and preconditioning, edge elements, vector potential, and so on, are unnecessary. This book introduces the basic theory of the least-squares method for first-order PDE systems, particularly the div-curl system and the div-curl-grad system. It is applied to the study of permissible boundary conditions for the incompressible Navier--Stokes equations, to show that the divergence equations in the Maxwell equations are not redundant, and to derive equivalent second-order versions of the Navier--Stokes equations and the Maxwell equations. This book covers diverse applications such as incompressible viscous flows, rotational inviscid flows, low- or high-Mach-number compressible flows, two-fluid flows, convective flows, and scattering waves.

Mathematical statistics --- Differential equations, Partial --- -Electromagnetism --- -Finite element method --- Fluid mechanics --- -Least squares --- 519.6 --- 681.3 *G18 --- Method of least squares --- Squares, Least --- Curve fitting --- Geodesy --- Mathematics --- Probabilities --- Triangulation --- Hydromechanics --- Continuum mechanics --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis --- Electromagnetics --- Magnetic induction --- Magnetism --- Metamaterials --- Partial differential equations --- Numerical solutions --- Computational mathematics. Numerical analysis. Computer programming --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Electromagnetism --- Finite element method. --- Least squares. --- Numerical solutions. --- Mathematics. --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Physics. --- Continuum physics. --- Optics. --- Electrodynamics. --- Calculus of variations. --- Computer mathematics. --- Fluids. --- Numerical and Computational Physics, Simulation. --- Classical and Continuum Physics. --- Classical Electrodynamics. --- Calculus of Variations and Optimal Control; Optimization. --- Computational Science and Engineering. --- Fluid- and Aerodynamics. --- Hydraulics --- Mechanics --- Physics --- Hydrostatics --- Permeability --- Computer mathematics --- Electronic data processing --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Dynamics --- Light --- Classical field theory --- Continuum physics --- Natural philosophy --- Philosophy, Natural --- Physical sciences

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Wave equation --- Scattering (Physics) --- Helmholtz equation --- Boundary value problems --- Finite element method --- Mathematical models --- Numerical solutions --- Finite element method. --- Wave equation. --- Numerical solutions. --- Mathematical models. --- -Helmholtz equation --- -Boundary value problems --- -Finite element method --- 681.3 *G18 --- 681.3 *G18 Partial differential equations: difference methods elliptic equations finite element methods hyperbolic equations method of lines parabolic equations (Numerical analysis) --- Partial differential equations: difference methods elliptic equations finite element methods hyperbolic equations method of lines parabolic equations (Numerical analysis) --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Boundary conditions (Differential equations) --- Reduced wave equation --- Wave equation, Reduced --- Atomic scattering --- Atoms --- Nuclear scattering --- Particles (Nuclear physics) --- Scattering of particles --- Wave scattering --- Scattering --- Boundary value problems -- Numerical solutions. --- Helmholtz equation -- Numerical solutions. --- Scattering (Physics) -- Mathematical models. --- Mathematics. --- Computer science --- Mathematical analysis. --- Analysis (Mathematics). --- Numerical analysis. --- Computational intelligence. --- Analysis. --- Numerical Analysis. --- Mathematics of Computing. --- Computational Intelligence. --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Differential equations, Partial --- Wave-motion, Theory of --- Numerical analysis --- Isogeometric analysis --- Collisions (Nuclear physics) --- Particles --- Collisions (Physics) --- Global analysis (Mathematics). --- Computer science. --- Engineering. --- Computer science—Mathematics. --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Mathematical analysis --- 517.1 Mathematical analysis --- Scattering (Physics) - Mathematical models --- Helmholtz equation - Numerical solutions --- Boundary value problems - Numerical solutions