Analysis of Adaptive Two-Grid Finite Element Algorithms for Linear and Nonlinear Problems
نویسندگان
چکیده
This paper proposes some efficient and accurate adaptive two-grid (ATG) finite element algorithms for linear nonlinear PDEs. The main idea of these is to utilize the solutions on $k$th-level meshes find $(k+1)$th-level which are constructed by performing bisections meshes. These transform nonsymmetric positive definite (non-SPD) PDEs (resp., PDEs) into symmetric (SPD) PDEs). proposed both due following advantages: They do not need solve or systems; degrees freedom very small, they easily implemented, interpolation errors small. Next, this constructs residual-type a posteriori error estimators shown be reliable efficient. key ingredient in proving efficiency establish an upper bound oscillation terms, may higher-order terms low regularity numerical solution. Furthermore, convergence proved when bisection used mesh refinements. Finally, experiments provided verify accuracy ATG compared regular [J. Xu, SIAM J. Numer. Anal., 33 (1996), pp. 1759--1777].
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2021
ISSN: ['1095-7197', '1064-8275']
DOI: https://doi.org/10.1137/19m1285615