A residual a posteriori error estimate for the Virtual Element Method

被引：33
|
作者：
Berrone, Stefano [1 ]
Borio, Andrea [1 ]
机构：
[1] Politecn Torino, Dipartimento Sci Matemat, Corso Duca Abruzzi 24, I-10129 Turin, Italy
来源：
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2017年 / 27卷 / 08期
关键词：
A posteriori" error estimates; Virtual Element Method; mesh adaptivity; Single-phase flows; underground flow simulations; CONSTRAINED OPTIMIZATION FORMULATION; FRACTURE NETWORK SIMULATIONS; ADVECTION-DIFFUSION PROBLEMS; ELLIPTIC PROBLEMS; DISCONTINUOUS COEFFICIENTS; HEAT-EQUATION; PARABOLIC EQUATIONS; POLYGONAL ELEMENTS; FLOW SIMULATIONS; DISCRETIZATIONS;
D O I：
10.1142/S0218202517500233
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A residual-based a posteriori error estimate for the Poisson problem with discontinuous diffusivity coefficient is derived in the case of a virtual element discretization. The error is measured considering a suitable polynomial projection of the discrete solution to prove an equivalence between the defined error and a computable residual based error estimator that does not involve any term related to the virtual element stabilization. Numerical results display a very good behavior of the ratio between the error and the error estimator, resulting independent of the meshsize and element distortion.
引用
收藏
页码：1423 / 1458
页数：36
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