We consider the lowest-order Raviart–Thomas mixed finite element
method for second-order elliptic problems on simplicial meshes in
two and three space dimensions. This method produces saddle-point
problems for scalar and flux unknowns. We show how to easily and
locally eliminate the flux unknowns, which implies the equivalence
between this method and a particular multi-point finite volume
scheme, without any approximate numerical integration. The matrix
of the final linear system is sparse, positive...
From the fundamental laws of elasticity, we write a model for the contact between two membranes and we perform the analysis of the corresponding system of variational inequalities. We propose a finite element discretization of this problem and prove its well-posedness. We also establish a priori and a posteriori error estimates.
From the fundamental laws of elasticity, we write a model for the contact between two membranes and we perform the analysis of the corresponding system of variational inequalities. We propose a finite element discretization of this problem and prove its well-posedness. We also establish and error estimates.
We derive error estimates for singularly
perturbed reaction–diffusion problems which yield a guaranteed
upper bound on the discretization error and are fully and easily
computable. Moreover, they are also locally efficient and robust in
the sense that they represent local lower bounds for the actual
error, up to a generic constant independent in particular of the
reaction coefficient. We present our results in the framework of
the vertex-centered finite volume method but their nature is
general...
Download Results (CSV)