Computational Methods in Engineering: A Variety of Primal & Mixed Methods, with Global & Local Interpolations, for Well-Posed or Ill-Posed BCs
L. Dong1, A. Alotaibi2, S.A. Mohiuddine2, S. N. Atluri3
CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.1, pp. 1-85, 2014, DOI:10.3970/cmes.2014.099.001
Abstract In this expository article, a variety of computational methods, such as Collocation, Finite Volume, Finite Element, Boundary Element, MLPG (Meshless Local Petrov Galerkin), Trefftz methods, and Method of Fundamental Solutions, etc., which are often used in isolated ways in contemporary literature are presented in a unified way, and are illustrated to solve a 4th order ordinary differential equation (beam on an elastic foundation). Both the primal formulation, which considers the 4th order ODE with displacement as the primitive variable, as well as two types of mixed formulations (one resulting in a set of 2 second-order ODEs, and the other resulting… More >
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