Convergence of a FEM and two-grid algorithms for elliptic problems on disjoint domains

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article

Jovanovic, Bosko S.²  Koleva, Miglena N.¹  Vulkov, Lubin G.¹ 

[1] Rousse Univ, Fac Nat Sci & Educ, Rousse 7017, Bulgaria

[2] Univ Belgrade, Fac Math, Belgrade 11000, Serbia

关键词: Convergence;    Disjoint domains;    Finite element method;    Stationary heat radiative problems;    Superconvergence;    Two-grid method;   

DOI  :  10.1016/j.cam.2011.07.019

来源: Elsevier

【 摘 要 】

In this paper, we analyze a FEM and two-grid FEM decoupling algorithms for elliptic problems on disjoint domains. First, we study the rate of convergence of the FEM and, in particular, we obtain a superconvergence result. Then with proposed algorithms, the solution of the multi-component domain problem (simple example two disjoint rectangles) on a fine grid is reduced to the solution of the original problem on a much coarser grid together with solution of several problems (each on a single-component domain) on fine meshes. The advantage is the computational cost although the resulting solution still achieves asymptotically optimal accuracy. Numerical experiments demonstrate the efficiency of the algorithms. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free