# Numerical Analysis

## 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…

## Global Random Walk Solutions for Flow and Transport in Porous Media

AbstractThis article presents a new approach to solve the equations of flow in heterogeneous porous media by using random walks…

## Unique continuation problems and stabilised finite element methods

Book summaryNumerical analysis for partial differential equations (PDEs) traditionally considers problems that are well-posed in the continuum, for example the…

## How many steps still left to x*?

Abstract The high speed of $$x_{k}\rightarrow x^\ast\in{\mathbb R}$$ is usually measured using the C-, Q- or R-orders: \tag{$C$} \lim \frac…

## Asymptotic analysis of a structure-preserving integrator for damped Hamiltonian systems

AbstractThe present work deals with the numerical long-time integration of damped Hamiltonian systems. The method that we analyze combines a…

## Global random walk solvers for fully coupled flow and transport in saturated/unsaturated porous media

AbstractIn this article, we present new random walk methods to solve flow and transport problems in saturated/unsaturated porous media, including coupled flow…

## Accurate spectral collocation computations of high order eigenvalues for singular Schrödinger equations-revisited

AbstractIn this paper, we continue to solve as accurately as possible singular eigenvalues problems attached to the Schrödinger equation. We…

## Accurate spectral collocation solutions to 2nd-order Sturm–Liouville problems

AbstractThis work is about the use of some classical spectral collocation methods as well as with the new software system…

## Accurate spectral collocation computation of high order eigenvalues for singular Schrödinger equations

AbstractWe are concerned with the study of some classical spectral collocation methods, mainly Chebyshev and sinc as well as with…