Triangular elements in the finite element method

Authors:
James H. Bramble and Miloš Zlámal

Journal:
Math. Comp. **24** (1970), 809-820

MSC:
Primary 65.66

DOI:
https://doi.org/10.1090/S0025-5718-1970-0282540-0

MathSciNet review:
0282540

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Abstract | References | Similar Articles | Additional Information

Abstract: For a plane polygonal domain $\Omega$ and a corresponding (general) triangulation we define classes of functions ${p_m}(x,y)$ which are polynomials on each triangle and which are in ${C^{(m)}}(\Omega )$ and also belong to the Sobolev space $W_2^{(m + 1)}(\Omega )$. 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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Additional Information

Keywords:
Finite element method,
Ritz method,
Galerkin method,
piecewise polynomial subspaces,
approximation of solution,
elliptic boundary problems

Article copyright:
© Copyright 1970
American Mathematical Society