Geodesic
Finite element analysis of primal and dual variational formulations of semicoercive elliptic problems with nonhomogeneous obstacles on the boundary
Applications of Mathematics, Tome 33 (1988) no. 1, pp. 1-21
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The Poisson equation with non-homogeneous unilateral condition on the boundary is solved by means of finite elements. The primal variational problem is approximated on the basis of linear triangular elements, and $O(h)$-convergence is proved provided the exact solution is regular enough. For the dual problem piecewise linear divergence-free approximations are employed and $O(h^{3/2})$-convergence proved for a regular solution. Some a posteriori error estimates are also presented.
The Poisson equation with non-homogeneous unilateral condition on the boundary is solved by means of finite elements. The primal variational problem is approximated on the basis of linear triangular elements, and $O(h)$-convergence is proved provided the exact solution is regular enough. For the dual problem piecewise linear divergence-free approximations are employed and $O(h^{3/2})$-convergence proved for a regular solution. Some a posteriori error estimates are also presented.
DOI : 10.21136/AM.1988.104282
Classification : 35J05, 65N15, 65N30
Keywords: semi-coercive elliptic problems; Poisson equation; finite elements; convergence; dual problem; a posteriori error estimates; variational inequalities 
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Tran, Van Bon. Finite element analysis of primal and dual variational formulations of semicoercive elliptic problems with nonhomogeneous obstacles on the boundary. Applications of Mathematics, Tome 33 (1988) no. 1, pp. 1-21. doi: 10.21136/AM.1988.104282

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