Geodesic
A finite element convergence analysis for 3D Stokes equations in case of variational crimes
Applications of Mathematics, Tome 45 (2000) no. 2, pp. 99-129 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We investigate a finite element discretization of the Stokes equations with nonstandard boundary conditions, defined in a bounded three-dimensional domain with a curved, piecewise smooth boundary. For tetrahedral triangulations of this domain we prove, under general assumptions on the discrete problem and without any additional regularity assumptions on the weak solution, that the discrete solutions converge to the weak solution. Examples of appropriate finite element spaces are given.
We investigate a finite element discretization of the Stokes equations with nonstandard boundary conditions, defined in a bounded three-dimensional domain with a curved, piecewise smooth boundary. For tetrahedral triangulations of this domain we prove, under general assumptions on the discrete problem and without any additional regularity assumptions on the weak solution, that the discrete solutions converge to the weak solution. Examples of appropriate finite element spaces are given.
DOI : 10.1023/A:1022235512626
Classification : 35Q30, 65N30
Keywords: Stokes equations; nonstandard boundary conditions; finite element method; approximation of boundary 
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     author = {Knobloch, Petr},
     title = {A finite element convergence analysis for {3D} {Stokes} equations in case of variational crimes},
     journal = {Applications of Mathematics},
     pages = {99--129},
     year = {2000},
     volume = {45},
     number = {2},
     doi = {10.1023/A:1022235512626},
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     zbl = {1067.65129},
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     url = {http://geodesic.mathdoc.fr/articles/10.1023/A:1022235512626/}
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Knobloch, Petr. A finite element convergence analysis for 3D Stokes equations in case of variational crimes. Applications of Mathematics, Tome 45 (2000) no. 2, pp. 99-129. doi: 10.1023/A:1022235512626

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