Several a posteriori error estimators for mortar mixed finite element discretizations of elliptic equations are derived. A residual-based estimator provides optimal upper and lower bounds for the pressure error. An efficient and reliable estimator for the velocity and mortar pressure error is also derived, which is based on solving local (element) problems in a higher-order space. The interface...

The stability and error estimates for the mortar finite element method are well established. This work examines the dependence of constants in these estimates on shape and number of subdomains. By means of a Poincaré inequality and some scaling arguments, these estimates are found not to deteriorate with increase in number of subdomains.

Guarantee of the strength for an aging structure, especially for a concrete structure, has been required. Possibility of the evaluation of a concrete structure using ultrasonic velocity has been investigated in civil engineering field in Japan. However, because the concrete is the complicate composite material which contains aggregates in mortar, and the ultrasonic propagation becomes complicat...

We consider the solution of the discrete linear system resulting from a mixed finite element discretization applied to a second-order elliptic boundary value problem in three dimensions. Based on a decomposition of the velocity space, these equations can be reduced to a discrete elliptic problem by eliminating the pressure through the use of substructures of the domain. The practicality of the ...

This paper is concerned with the mortar finite element method for three spatial variables. The two main issues are the proof of the LBB condition based on appropriate choices of Lagrange multipliers and optimal efficiency of corresponding multigrid schemes for the whole coupled systems of equations. The implementation of the smoothing procedure also differs from that one used in the 2-dimension...

Discrete Mechanics based on finite element methods is presented in this paper. We also explore the relationship between this discrete mechanics and Veselov discrete mechanics. High order discretizations are constructed in terms of high order interpolations.

We consider the Poisson equation with Dirichlet boundary conditions on a polygonal domain with one reentrant corner. We introduce new nonconforming finite element discretizations based on mortar techniques and singular functions. The main idea introduced in this paper is the replacement of cut-off functions by mortar element techniques on the boundary of the domain. As advantages, the new discr...

and Applied Analysis 3 Let EI and EB be the set of interior edges and boundary edges of Th, respectively. Let E EI ∪ EB. Denote by v the restriction of v to Ki. Let e eij ∈ EI with i > j. Then we denote the jump v and the average {v} of v on e by v |e v ∣ ∣ ∣ e −v ∣ ∣ ∣ e , {v}|e 1 2 ( v ∣ ∣ ∣ e v ∣ ∣ ∣ e ) . 2.4 If e ei ∈ EB, we denote v and {v} of v on e by v |e {v}|e v ∣ ∣ ∣ e . 2.5