50 citations · 130 across the 16 of their papers we have counts for
17 papers
Goal-oriented adaptivity for multilevel stochastic Galerkin FEM with nonlinear goal functionals
Alex Bespalov, Dirk Praetorius, Michele Ruggeri
This paper is concerned with the numerical approximation of quantities of interest associated with solutions to parametric elliptic partial differential equations (PDEs). The key n…
Error estimation and adaptivity for stochastic collocation finite elements Part II: multilevel approximation
Alex Bespalov, David J. Silvester
A multilevel adaptive refinement strategy for solving linear elliptic partial differential equations with random data is recalled in this work. The strategy extends the a posterior…
Error estimation and adaptivity for stochastic collocation finite elements Part I: single-level approximation
Alex Bespalov, David Silvester, Feng Xu
A general adaptive refinement strategy for solving linear elliptic partial differential equation with random data is proposed and analysed herein. The adaptive strategy extends the…
Two-level a posteriori error estimation for adaptive multilevel stochastic Galerkin FEM
Alex Bespalov, Dirk Praetorius, Michele Ruggeri
The paper considers a class of parametric elliptic partial differential equations (PDEs), where the coefficients and the right-hand side function depend on infinitely many (uncerta…
T-IFISS: a toolbox for adaptive FEM computation
Alex Bespalov, Leonardo Rocchi, David Silvester
T-IFISS is a finite element software package for studying finite element solution algorithms for deterministic and parametric elliptic partial differential equations. The emphasis…
A posteriori error estimation and adaptivity in stochastic Galerkin FEM for parametric elliptic PDEs: beyond the affine case
Alex Bespalov, Feng Xu
We consider a linear elliptic partial differential equation (PDE) with a generic uniformly bounded parametric coefficient. The solution to this PDE problem is approximated in the f…
Convergence of adaptive stochastic Galerkin FEM
Alex Bespalov, Dirk Praetorius, Leonardo Rocchi +1
We propose and analyze novel adaptive algorithms for the numerical solution of elliptic partial differential equations with parametric uncertainty. Four different marking strategie…
Robust a posteriori error estimation for stochastic Galerkin formulations of parameter-dependent linear elasticity equations
Arbaz Khan, Alex Bespalov, Catherine E. Powell +1
The focus of this work is a posteriori error estimation for stochastic Galerkin approximations of parameter-dependent linear elasticity equations. The starting point is a three-fie…
Adaptive BEM with optimal convergence rates for the Helmholtz equation
Alex Bespalov, Timo Betcke, Alexander Haberl +1
We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is…
Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs
Alex Bespalov, Dirk Praetorius, Leonardo Rocchi +1
We use the ideas of goal-oriented error estimation and adaptivity to design and implement an efficient adaptive algorithm for approximating linear quantities of interest derived fr…
Adaptive FEM with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems
Alex Bespalov, Alexander Haberl, Dirk Praetorius
We prove that for compactly perturbed elliptic problems, where the corresponding bilinear form satisfies a Garding inequality, adaptive mesh-refinement is capable of overcoming the…
Natural hp-BEM for the electric field integral equation with singular solutions
Alexei Bespalov, Norbert Heuer
We apply the hp-version of the boundary element method (BEM) for the numerical solution of the electric field integral equation (EFIE) on a Lipschitz polyhedral surface G. The unde…
A new H(div)-conforming p-interpolation operator in two dimensions
Alexei Bespalov, Norbert Heuer
In this paper we construct a new H(div)-conforming projection-based p-interpolation operator that assumes only -regularity (r > 0) on the refere…
Convergence of the Natural hp-BEM for the Electric Field Integral Equation on Polyhedral Surfaces
Alexei Bespalov, Norbert Heuer, Ralf Hiptmair
We consider the variational formulation of the electric field integral equation (EFIE) on bounded polyhedral open or closed surfaces. We employ a conforming Galerkin discretization…
The hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces: a priori error analysis
Alexei Bespalov, Norbert Heuer
This paper presents an a priori error analysis of the hp-version of the boundary element method for the electric field integral equation on a piecewise plane (open or closed) Lipsc…
Optimal error estimation for H(curl)-conforming p-interpolation in two dimensions
Alexei Bespalov, Norbert Heuer
In this paper we prove an optimal error estimate for the H(curl)-conforming projection based p-interpolation operator introduced in [L. Demkowicz and I. Babuska, p interpolation er…
On the convergence of the hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces
Alexei Bespalov, Norbert Heuer
In this paper the hp-version of the boundary element method is applied to the electric field integral equation on a piecewise plane (open or closed) Lipschitz surface. The underlyi…