Triangular elements in the finite element method
1970; American Mathematical Society; Volume: 24; Issue: 112 Linguagem: Inglês
10.1090/s0025-5718-1970-0282540-0
ISSN1088-6842
AutoresJames H. Bramble, Milos̋ Zlámal,
Tópico(s)Numerical methods in inverse problems
ResumoFor a plane polygonal domain Ω \Omega and a corresponding (general) triangulation we define classes of functions p m ( x , y ) {p_m}(x,y) which are polynomials on each triangle and which are in C ( m ) ( Ω ) {C^{(m)}}(\Omega ) and also belong to the Sobolev space W 2 ( m + 1 ) ( Ω ) W_2^{(m + 1)}(\Omega ) . Approximation theoretic properties are proved concerning these functions. These results are then applied to the approximate solution of arbitrary-order elliptic boundary value problems by the Galerkin method. Estimates for the error are given. The case of second-order problems is discussed in conjunction with special choices of approximating polynomials.
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