Definitions
Weighted residual methods (WRMs) are methods for solving partial differential equations (PDEs). The approximate solution is represented as a finite series of linearly independent basis functions and obtained by minimizing an integral error. Weighted residual methods allow to derive the classical approximation methods, i.e., finite difference methods (FDMs), finite element methods (FEMs), and boundary element methods (BEMs).
Basic Definitions and Classification of Approximate Methods
Physical phenomena and processes are typically described by equations, particularly by partial differential equations (Debnath, 2012; Formaggia et al., 2012; Salsa, 2008). Various solution strategies are suggested in the literature to solve such equations or systems of equations (Bartels, 2016; Formaggia et al., 2012; Le Dret and Lucquin, 2016). In engineering practice, the finite element method...
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References
Bartels S (2016) Numerical approximation of partial differential equations. Springer, Cham
Bathe K-J (1996) Finite element procedures. Prentice-Hall, Upper Saddle River
Blaauwendraad J (2010) Plates and FEM: surprises and pitfalls. Springer, Dordrecht
Brebbia CA, Connor JJ (1974) Fundamentals of finite element techniques for structural engineers. Wiley, New York
Brebbia CA, Telles JCF, Wrobel LC (1984) Boundary element techniques: theory and applications in engineering. Springer, Berlin
Bruhns OT (2003) Advanced mechanics of solids. Springer, Berlin
Budynas RG (1999) Advanced strength and applied stress analysis. McGraw-Hill Book, Singapore
Debnath L (2012) Nonlinear partial differential equations for scientists and engineers. Springer, New York
Fish J, Belytschko T (2007) A first course in finite elements. Wiley, Chichester
Formaggia L, Saleri F, Veneziani A (2012) Solving numerical PDEs: problems, applications, exercises. Springer, Milan
Gross D, Hauger W, Schröder J, Wall WA, Bonet J (2011) Engineering mechanics 2: mechanics of materials. Springer, Berlin
Hartsuijker C, Welleman JW (2007) Engineering mechanics volume 2: stresses, strains, displacements. Springer, Dordrecht
Le Dret H, Lucquin B (2016) Partial differential equations: modeling, analysis and numerical approximation. Birkhäuser, Basel
Öchsner A (2016) Computational statics and dynamics: an introduction based on the finite element method. Springer, Singapore
Öchsner A, Merkel M (2013) One-dimensional finite elements: an introduction to the FE method. Springer, Berlin
Reddy JN (2006) An introduction to the finite element method. McGraw Hill, Singapore
Salsa S (2008) Partial differential equations in action: from modelling to theory. Springer, Milano
Timoshenko SP (1940) Strength of materials – Part I elementary theory and problems. D Van Nostrand Company, New York
Wang CM, Reddy JN, Lee KH (2000) Shear deformable beams and plates: relationships with classical solution. Elsevier, Oxford
Zienkiewicz OC, Taylor RL (2000) The finite element method. Volume 1: the basis. Butterworth-Heinemann, Oxford
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Öchsner, A. (2018). Weighted Residual Methods for Finite Elements. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_20-1
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DOI: https://doi.org/10.1007/978-3-662-53605-6_20-1
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