Geodesic
Penalty method and extrapolation for axisymmetric elliptic problems with Dirichlet boundary conditions
Applications of Mathematics, Tome 35 (1990) no. 5, pp. 405-417.

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A second order elliptic problem with axisymmetric data is solved in a finite element space, constructed on a triangulation with curved triangles, in such a way, that the (nonhomogeneous) boundary condition is fulfilled in the sense of a penalty. On the basis of two approximate solutions, extrapolates for both the solution and the boundary flux are defined. Some a priori error estimates are derived, provided the exact solution is regular enough. The paper extends some of the results of J.T. King [6], [7].
DOI : 10.21136/AM.1990.104420
Classification : 35J25, 65N15, 65N30, 73K25
Keywords: finite elements; penalty method; axisymmetric problems; extrapolation; a priori error estimates 
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     author = {Hlav\'a\v{c}ek, Ivan},
     title = {Penalty method and extrapolation for axisymmetric elliptic problems with {Dirichlet} boundary conditions},
     journal = {Applications of Mathematics},
     pages = {405--417},
     publisher = {mathdoc},
     volume = {35},
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     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1990.104420/}
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Hlaváček, Ivan. Penalty method and extrapolation for axisymmetric elliptic problems with Dirichlet boundary conditions. Applications of Mathematics, Tome 35 (1990) no. 5, pp. 405-417. doi : 10.21136/AM.1990.104420. http://geodesic.mathdoc.fr/articles/10.21136/AM.1990.104420/

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