Triangular Elements in the Finite Element Method

作者：James H. Bramble, Miloš Zlámal · 发表于：Mathematics of Computation · 年份：1970 · DOI：10.2307/2004615 · 被引用次数：65 · 研究领域：Metallurgy and Material Forming、Mechanical and Thermal Properties Analysis、Metal Forming Simulation Techniques

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.