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Finite volume method for the variational inequalities of first and second kinds
Author(s) -
Zhang Tie,
Tang Lixin
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3331
Subject(s) - variational inequality , mathematics , obstacle problem , convergence (economics) , norm (philosophy) , finite volume method , obstacle , stability (learning theory) , error analysis , mathematical analysis , mathematical optimization , computer science , physics , machine learning , political science , mechanics , law , economics , economic growth
We propose and analyze the finite volume method for solving the variational inequalities of first and second kinds. The stability and convergence analysis are given for this method. For the elliptic obstacle problem, we derive the optimal error estimate in the H 1 ‐norm. For the simplified friction problem, we establish an abstract H 1 ‐error estimate, which implies the convergence if the exact solution u ∈ H 1 (Ω) and the optimal error estimate if u ∈ H 1 + α (Ω),0 < α ≤2. Copyright © 2015 John Wiley & Sons, Ltd.