Transient Problems

Prem K. Kythe and Dongming Wei
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Prem K. Kythe: University of New Orleans, Department of Mathematics
Dongming Wei: University of New Orleans, Department of Mathematics

Chapter 9 in An Introduction to Linear and Nonlinear Finite Element Analysis, 2004, pp 207-240 from Springer

Abstract: Abstract We discuss the finite element analysis of one- and two-dimensional transient problems by using a semidiscrete weighted residual method and approximating the solution u by taking $$ u(x,t) \approx \sum\nolimits_{i = 1}^n {} u_i^e \left( t \right)\varphi _i^e \left( x \right) $$ in the one-dimensional case, and taking $$ u(x,y,t) \approx \sum\nolimits_{i = 1}^n {} u_i^e \left( t \right)\varphi _i^e \left( {x,y} \right) $$ in two-dimensional case, where $$ \varphi _i^{\left( e \right)} $$ are the interpolating shape functions, and $$ u_i^{(e)} $$ are determined by finite difference methods.

Keywords: Exact Solution; Finite Element Solution; Essential Boundary Condition; Finite Element Equation; Transient Problem (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-8160-9_9

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DOI: 10.1007/978-0-8176-8160-9_9

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