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…
Finite element (FEM)
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…
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…
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…
A Constructive Introduction to Finite Elements Method
Book summarySummary of the book… Book coverKeywordskeyword1, Contents1.Variational formulations 1.1. A 1D model problem 1.2. A 2D model problem (lapace…
Finite Element Method and Applications
Book summarySummary of the book… Book cover Contents clickableIntroduction by Acad. Caius Iacob Foreword Functional Analysis Itinerary 1.1. Vector spaces.…
Numerical benchmark study for flow in highly heterogeneous aquifers
AbstractThis article presents numerical investigations on accuracy and convergence properties of several numerical approaches for simulating steady state flows in…
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…
A stabilized finite element method for inverse problems subject to the convection-diffusion equation. I: diffusion-dominated regime
AbstractThe numerical approximation of an inverse problem subject to the convection–diffusion equation when diffusion dominates is studied. We derive Carleman…