Approximation of Some Function Spaces by Finite Element Methods

Roger Temam

Chapter Chapter 10 in Numerical Analysis, 1973, pp 80-104 from Springer

Abstract: Abstract In this chapter we study the approximation of the space H 0 1 (Ω) by finite element methods. In finite element methods the approximating functions are not step functions, but functions defined on a set of n-simplices contained in Ω Inside the simplex the approximating function is a simple function, a linear function in the simplest case, or some type of polynomial function of restricted degree in more refined situations. We will only consider approximation by piecewise linear functions. In this case the approximation is said to be conforming or non-conforming according as the approximating functions are continuous or some kind of discontinuities are allowed at the boundaries of the simplices. We will give some preliminary results in Section 10.1 and then study these two approximations in Sections 10.2 and 10.3.

Keywords: Finite Element Method; APPROXIMA TION; Piecewise Linear Function; Dense Subspace; Nonconforming Finite Element (search for similar items in EconPapers)
Date: 1973
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DOI: 10.1007/978-94-010-2565-2_11

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