We design and analyze multigrid methods for the saddle point problems resulting from Raviart-Thomas-Nédélec mixed finite element methods (of order at least 1) for the Darcy system in porous media flow. Uniform convergence of the W -cycle algorithm in a nonstandard energy norm is established. Extensions to general second order elliptic problems are also addressed.

A multigrid algorithm for saddle point problems arising from mortar nite element discretizations is analyzed. Here, we do not require that the constraints at the interface are satissed in each smoothing step. Using mesh dependent norms for the Lagrange multiplier, suitable approximation and smoothing properties are established. A convergence rate independent of the meshsize is obtained for the ...

In this paper we consider multigrid algorithms for nonconforming and mixed nite element methods for second order elliptic problems on triangular and rectangular nite elements. We prove optimal convergence properties of the W-cycle multigrid algorithm and uniform condition number estimates for the variable V-cycle preconditioner. Lower order terms are treated, so our results also apply to parabo...

In this paper, a multigrid algorithm is studied for mortar element method for rotated Q1 element, the mortar condition is only dependent on the degrees of the freedom on subdomains interfaces. We prove the convergence of W-cycle multigrid and construct a variable V-cycle multigrid preconditioner which is available.

Plant adaptations to the environment are limited, and therefore plants in similar environments may display similar functional and physiological traits, a pattern termed functional convergence. Evidence was examined for functional convergence among 28 evergreen woody shrubs from three plant communities of the semi-arid winter rainfall region of southern California. Both leaf and water relations ...

This paper considers estimation of sparse covariance matrices and establishes the optimal rate of convergence under a range of matrix operator norm and Bregman divergence losses. A major focus is on the derivation of a rate sharp minimax lower bound. The problem exhibits new features that are significantly different from those that occur in the conventional nonparametric function estimation pro...

We consider functionals of the form F (u) = ∫ f(x,Du) dμ ( u ∈ D(R) ) where μ is a finite Borel measure on R, and their relaxation F with respect to the weak convergence of a suitable Sobolev space W 1,p μ . Applications to low dimensional structures and junctions are given.

Let A be à transcendental entire function of order < 1. If w, and w2 are two linearly independent solutions of the differential equation y" + A y — 0, then at least one of wl, w2 has the property that the exponent of convergence of its zeros is > 1.

In the robot navigation problem, noisy sensor data must be filtered to obtain the best estimate of the robot position. W e propose using a Recursive Total Least Squares algorithm t o obtain estimates of the robotposition. W e avoid several weaknesses inherent in the use of the Kalman and extended Ka lman filters, achieving much faster convergence without good initial (a priori) estimates of the...

In a recent work by the author an extrapolation method, the W-transformation, was developed, by which a large class of oscillatory infinite integrals can be computed very efficiently. The results of this work are extended to a class of divergent oscillatory infinite integrals in the present paper. It is shown in particular that these divergent integrals exist in the sense of Abel summability an...