A parallel multigrid method using the full domain partition.
A parallel projection method for linear algebraic systems
A direct projection method for solving systems of linear algebraic equations is described. The algorithm is equivalent to the algorithm for minimization of the corresponding quadratic function and can be generalized for the minimization of a strictly convex function.
A Parallel Projection Method for Solving Generalized Linear Least-Squares Problems.
A parallel QR-factorization/solver of quasiseparable matrices.
A parallel splitting-up method for partial differential equations and its applications to Navier-Stokes equations
A parameter choice for Tikhonov regularization for solving nonlinear inverse problems leading to optimal convergence rates
We give a derivation of an a-posteriori strategy for choosing the regularization parameter in Tikhonov regularization for solving nonlinear ill-posed problems, which leads to optimal convergence rates. This strategy requires a special stability estimate for the regularized solutions. A new proof fot this stability estimate is given.
A parameter choice method for Tikhonov regularization.
A parameter robust method for singularly perturbed delay differential equations.
A parameter-free smoothness indicator for high-resolution finite element schemes
This paper presents a postprocessing technique for estimating the local regularity of numerical solutions in high-resolution finite element schemes. A derivative of degree p ≥ 0 is considered to be smooth if a discontinuous linear reconstruction does not create new maxima or minima. The intended use of this criterion is the identification of smooth cells in the context of p-adaptation or selective flux limiting. As a model problem, we consider a 2D convection equation discretized with bilinear finite...
A parameter-free stabilized finite element method for scalar advection-diffusion problems
We formulate and study numerically a new, parameter-free stabilized finite element method for advection-diffusion problems. Using properties of compatible finite element spaces we establish connection between nodal diffusive fluxes and one-dimensional diffusion equations on the edges of the mesh. To define the stabilized method we extend this relationship to the advection-diffusion case by solving simplified one-dimensional versions of the governing equations on the edges. Then we use H(curl)-conforming...
A parameterized lower bound for the smallest singular value.
A parametrized Newton method for nonsmooth equations with finitely many maximum functions
In this paper we propose a parametrized Newton method for nonsmooth equations with finitely many maximum functions. The convergence result of this method is proved and numerical experiments are listed.
A partially ordered space connected with the de la Vallée Poussin problem
A Particle Method for First-order Symmetric Systems.
A particular smooth interpolation that generates splines
There are two grounds the spline theory stems from - the algebraic one (where splines are understood as piecewise smooth functions satisfying some continuity conditions) and the variational one (where splines are obtained via minimization of some quadratic functionals with constraints). We use the general variational approach called smooth interpolation introduced by Talmi and Gilat and show that it covers not only the cubic spline and its 2D and 3D analogues but also the well known tension spline...
A penalized bandit algorithm.
A penalty approach for a box constrained variational inequality problem
We propose a penalty approach for a box constrained variational inequality problem . This problem is replaced by a sequence of nonlinear equations containing a penalty term. We show that if the penalty parameter tends to infinity, the solution of this sequence converges to that of when the function involved is continuous and strongly monotone and the box contains the origin. We develop the algorithmic aspect with theoretical arguments properly established. The numerical results tested on...
A penalty method for approximations of the stationary power-law Stokes problem.
A Penalty Method for the Approximate Solution of Stationary Maxwell Equations.
A penalty method for the time-dependent Stokes problem with the slip boundary condition and its finite element approximation
We consider the finite element method for the time-dependent Stokes problem with the slip boundary condition in a smooth domain. To avoid a variational crime of numerical computation, a penalty method is introduced, which also facilitates the numerical implementation. For the continuous problem, the convergence of the penalty method is investigated. Then we study the fully discretized finite element approximations for the penalty method with the P1/P1-stabilization or P1b/P1 element. For the discretization...