Abstract:
The paper is devoted to the mixed finite element method for the equation $\Delta\Delta u+\kappa^2u=f$, $x\in\Omega$, with boundary conditions $u=\partial u/\partial\nu=0$ on $\partial\Omega$, where $\nu$ is the normal to the boundary and $\kappa\geqslant0$ is an arbitrary constant on each finite element. At $\kappa\equiv0$ residual type a posteriori error bounds for the mixed Ciarlet-Raviart method were derived by several authors at the use of different error norms. The bounds, termed sometimes a posteriori functional error majorants, seem to be less dependent on the constants in the general approximation bounds and are more flexible and adaptable for attaining higher accuracy at practical implementation. In this paper, we present a posteriori functional error majorants for the mixed Ciarlet-Raviart method in the case of $\kappa\ne0$ and having large jumps. Robustness and sharpness of the bounds are approved by the lower bounds of local efficiency.
Key words:a posteriori error bounds, singularly perturbed elliptic equations of $4$th order, mixed finite element method, lower error bounds.
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