APPROXIMATION THEORY FOR THE P-VERSION OF THE FINITE ELEMENT METHOD IN THREE DIMENSIONS PART II: CONVERGENCE OF THE P VERSION OF THE FINITE ELEMENT METHOD

作者：Guo Benqi^*

来源：SIAM Journal on Numerical Analysis, 2009, 47(4): 2578-2611.

DOI：10.1137/070701066

• p-version
• finite element method
• Jacobi-weighted Besov and Sobolev spaces
• Jacobi projection
• Chebyshev projection-interpolation
• tetrahedron
• hexahedron
• triangular prism

This paper is the second in a series devoted to the approximation theory of the p-version of the finite element method in three dimensions. In this paper, we analyze the approximability of functions in the framework of the Jacobi-weighted Besov and Sobolev spaces in the three-dimensional setting and approximation error of the p-version of the finite element method on meshes containing tetrahedral, hexahedral, and prism elements for elliptic problems with homogeneous and nonhomogeneous Dirichlet boundary condition. The convergence rate is rigorously proved for solutions in H(k)(Omega). The optimal convergence of the p-version for elliptic problems on polyhedral domains will be analyzed in the forthcoming Part III [B. Q. Guo, Approximation theory of the p-version of the finite element method in three dimensions, Part III: Optimal convergence for problems on polyhedral domains, in preparation] of the series.

• 出版日期2009
• 单位上海师范大学