Optimal multilevel methods for graded bisection grids
We design and analyze optimal additive and multiplicative multilevel methods for solving H 1 problems on graded grids obtained by bisection. We deal with economical local smoothers: after a global smoothing in the finest mesh, local smoothing for each ...
Interlacing of zeros of Gegenbauer polynomials of non-consecutive degree from different sequences
A theorem due to Stieltjes’ states that if $${\{p_n\}_{n=0}^\infty}$$ is any orthogonal sequence then, between any two consecutive zeros of p k , there is at least one zero of p n whenever k < n, a property called Stieltjes interlacing. We show that ...
Convergence rates for Tikhonov regularization of a two-coefficient identification problem in an elliptic boundary value problem
We investigate the convergence rates for Tikhonov regularization of the problem of simultaneously estimating the coefficients q and a in the Neumann problem for the elliptic equation $${{-{\rm div}(q \nabla u) + au = f \;{\rm in}\; \Omega, q{\partial u}/...
The maximum angle condition is not necessary for convergence of the finite element method
We show that the famous maximum angle condition in the finite element analysis is not necessary to achieve the optimal convergence rate when simplicial finite elements are used to solve elliptic problems. This condition is only sufficient. In fact, ...
Exponential decay of the power spectrum and finite dimensionality for solutions of the three dimensional primitive equations
In this article we estimate the number of modes, volumes and nodes, sufficient to describe well the solution of the three dimensional primitive equations; the physical meaning of these estimates is also discussed. We also study the exponential decay of ...
A domain decomposition method for solving the hypersingular integral equation on the sphere with spherical splines
We present an overlapping domain decomposition technique for solving the hypersingular integral equation on the sphere with spherical splines. We prove that the condition number of the additive Schwarz operator is bounded by O(H/δ), where H is the size ...
Finite difference methods for a nonlinear and strongly coupled heat and moisture transport system in textile materials
In this paper, we study heat and moisture transport through porous textile materials with phase change, described by a degenerate, nonlinear and strongly coupled parabolic system. An uncoupled finite difference method with semi-implicit Euler scheme in ...