We analyze residual and hierarchical a posteriori error estimates for nonconforming finite element approximations of elliptic problems with variable coefficients. We consider a finite volume box scheme equivalent to a nonconforming mixed finite element method in a Petrov–Galerkin setting. We prove that all the estimators yield global upper and local lower bounds for the discretization error. Finally, we present results illustrating the efficiency of the estimators, for instance, in the simulation...
We consider a system
of degenerate parabolic equations modelling a
thin film, consisting of two layers of immiscible Newtonian liquids, on
a solid horizontal substrate.
In addition, the model includes the presence of insoluble surfactants on
both the free liquid-liquid and liquid-air interfaces,
and the presence of both attractive and repulsive van der Waals forces
in terms of the heights of the two layers.
We show that this system formally satisfies a Lyapunov structure,
and a second energy...
We analyze residual and hierarchical
error estimates for nonconforming finite element
approximations of elliptic problems with variable coefficients.
We consider a finite volume box scheme equivalent to
a nonconforming mixed finite element method in a Petrov–Galerkin
setting. We prove that
all the estimators yield global upper and local lower bounds for the discretization
error. Finally, we present results illustrating the efficiency of the
estimators, for instance, in the simulation of Darcy...
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