Optimal approximation of unique continuation
Abstract We consider numerical approximations of ill-posed elliptic problems with conditional stability. The notion of optimal error estimates is defined including…
PDEs (numerical)
Theory and computation of radial solutions for Neumann problems with φ-Laplacian
Abstract The paper deals with existence, localization and multiplicity of radial positive solutions in the annulus or the ball, for…
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…
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…
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…
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…
Spectral collocation based on quasi-classical orthogonal polynomials applied to solve a singular BVP from Hydrodynamics
AbstractIt is well established that spectral collocation methods based on classical orthogonal polynomials, in spite of their high order accuracy,…
A stabilized finite element method for inverse problems subject to the convection-diffusion equation. II: convection-dominated regime
AbstractWe consider the numerical approximation of the ill-posed data assimilation problem for stationary convection–diffusion equations and extend our previous analysis…