Optimal finite element approximation of unique continuation
Abstract We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is…
(preprint)
Computational orders of convergence of iterative methods for Richards’ equation
Abstract Numerical solutions for flows in partially saturated porous media pose challenges related to the non-linearity and elliptic-parabolic degeneracy of…
Role of partial functionals in the study of variational systems
Abstract Applying techniques originally developed for systems lacking a variational structure, we establish conditions for the existence of solutions in…
On high-order conforming finite element methods for ill-posed Helmholtz problems
Abstract We consider the numerical approximation of the linear ill-posed problem of unique continuation for the Helmholtz equation. We first…
Tikhonov regularization of a perturbed heavy ball system with vanishing damping
AbstractThis paper deals with aa perturbed heavy ball system with vanishing damping that contains a Tikhonov regularization term, in connection…
Accurate spectral collocation solutions to some Bratu’s type boundary value problems
AbstractWe solve by Chebyshev spectral collocation some genuinely nonlinear Liouville-Bratu-Gelfand type, 1D and a 2D boundary value problems. The problems…
Inequalities for indices of coincidence and entropies
AbstractWe consider a probability distribution depending on a real parameter x. As functions of x, the Renyi entropy and the…
Benchmark for numerical solutions of flow in heterogeneous groundwater formations
AbstractThis article presents numerical investigations on accuracy and convergence properties of several numerical approaches for simulating steady state flows in…
The long time behavior and the rate of convergence of symplectic convex algorithms obtained via splitting discretizations of inertial damping systems
AbstractIn this paper we propose new numerical algorithms in the setting of unconstrained optimization problems and we give proof for…
Sheffer sequences, probability distributions and approximation operators
AbstractWe present a new method to compute formulas for the action on monomials of a generalization of binomial approximation operators…