Estimates of the Distance to Exact Solutions of the Stokes Problem with Slip and Leak Boundary Conditions

被引:0
作者
Neittaanmäki P. [1 ]
Nokka M. [1 ]
Repin S. [2 ,3 ]
机构
[1] Department of mathematical information technology, University of Jyväskylä, Jyväskylä
[2] V. A. Steklov Institute of Mathematics RAS, 27, Fontanka, St. Petersburg
[3] Peter the Great St. Petersburg Polytechnic University, 29, Polytekhnicheskaya St, St. Petersburg
关键词
D O I
10.1007/s10958-019-04477-6
中图分类号
学科分类号
摘要
We deduce a posteriori error estimates of functional type for the stationary Stokes problem with slip and leak boundary conditions. The derived error majorants do not contain mesh dependent constants and are valid for a wide class of energy admissible approximations that satisfy the Dirichlet boundary condition on a part of the boundary. Different forms of error majorants contain global constants associated with Poincaré type inequalities or the stability (LBB) condition for the Stokes problem or constants associated with subdomains (if a domain decomposition is applied). It is proved that the majorants are guaranteed and vanish if and only if the functions entering them coincide with the respective exact solutions. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.
引用
收藏
页码:280 / 298
页数:18
相关论文
共 38 条
[31]  
Ol'shanskij M.A., Chizhonkov E.V., On the domain geometry dependence of the LBB condition, Math. Model. Numer. Anal., 34, 5, pp. 935-951, (2000)
[32]  
Payne L.E., A bound for the optimal constant in an inequality of Ladyzhenskaya and Solonnikov, IMA J. Appl. Math., 72, 5, pp. 563-569, (2007)
[33]  
Mali O., Neittaanmaki P., Repin S., Accuracy Verification Methods. Theory and Algorithms, (2014)
[34]  
Ladyzhenskaya O.A., Ural'tseva N.N., Quasilinear elliptic equations and variational problems in several independent variables, Rus. Math. Surv., 16, 1, pp. 17-91, (1961)
[35]  
Ekeland I., Temam R., Convex Analysis and Variational Problems, (1976)
[36]  
Matculevich S., Repin S., Explicit constants in Poincaré-type inequalities for simplicial domains and application to a posteriori estimates, Comput. Methods Appl. Math., 16, 2, pp. 277-298, (2016)
[37]  
Nazarov A.I., Repin S.I., Exact constants in Poincaré type inequalities for functions with zero mean boundary traces, Math. Methods Appl. Sci., 38, 15, pp. 3195-3207, (2015)
[38]  
Repin S., Sysala S., Haslinger J., Computable majorants of the limit load in Hencky’s plasticity problems, Comput. Math. Appl., 75, 1, pp. 199-217, (2018)