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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. (English). Aplikace matematiky, vol. 33 (1988), issue 1, pp. 1-21
MSC: 35J05, 65N15, 65N30 | MR 0934370 | Zbl 0638.65077 | DOI: 10.21136/AM.1988.104282
Keywords:
semi-coercive elliptic problems; Poisson equation; finite elements; convergence; dual problem; a posteriori error estimates; variational inequalities
Summary:
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.
References:
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