Related papers: An equilibrated flux a posteriori error estimator …
The spectral deferred correction method is a variant of the deferred correction method for solving ordinary differential equations. A benefit of this method is that is uses low order schemes iteratively to produce a high order…
We present a simple method for \emph{a posteriori} removal of a significant fraction of the density-fitting error from the calculated total coupled-cluster energies. The method treats the difference between the exact and density-fitted…
This work proposes an adaptive framework to solve a robust structural shape optimization problem governed by linear elasticity models that account for uncertainties in the loading and material inputs. A posteriori error estimators are…
A convincing feature of least-squares finite element methods is the built-in a posteriori error estimator for any conforming discretization. In order to generalize this property to discontinuous finite element ansatz functions, this paper…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
We study image inverse problems with a normalizing flow prior. Our formulation views the solution as the maximum a posteriori estimate of the image conditioned on the measurements. This formulation allows us to use noise models with…
The issue of single-grid discretization error estimator, operating in the postprocessor mode, is addressed in the paper. An ensemble of numerical solutions, obtained using solvers of different accuracy, is shown to provide an upper estimate…
The flux-mortar mixed finite element method was recently developed for a general class of domain decomposition saddle point problems on non-matching grids. In this work we develop the method for Darcy flow using the multipoint flux…
We consider a finite volume scheme with two-point flux approximation (TPFA) to approximate a Laplace problem when the solution exhibits no more regularity than belonging to $H^1_0(\Omega)$. We establish in this case some error bounds for…
We present a framework that relates preconditioning with a posteriori error estimates in finite element methods. In particular, we use standard tools in subspace correction methods to obtain reliable and efficient error estimators. As a…
We present a posteriori error estimates for finite element approximations in a minimization approach to a coefficient inverse problem. The problem is that of reconstructing the dielectric permittivity $\varepsilon =…
A widely used electrostatics model in the biomolecular modeling community, the nonlinear Poisson-Boltzmann equation, along with its finite element approximation, are analyzed in this paper. A regularized Poisson-Boltzmann equation is…
Domain decomposition methods are widely used for the numerical solution of partial differential equations on high performance computers. We develop an adjoint-based a posteriori error analysis for both multiplicative and additive…
A new technique of residual-type a posteriori error analysis is developed for the lowest-order Raviart-Thomas mixed finite element discretizations of convection-diffusion-reaction equations in two- or three-dimension. Both centered mixed…
We consider the approximation of singularly perturbed linear second-order boundary value problems by $hp$-finite element methods. In particular, we include the case where the associated differential operator may not be coercive. Within this…
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 framework of stochastic Galerkin finite element methods. We…
In this paper, we will consider an $hp$-finite elements discretization of a highly indefinite Helmholtz problem by some dG formulation which is based on the ultra-weak variational formulation by Cessenat and Depr\'{e}s. We will introduce an…
This paper concerns a posteriori error analysis for the streamline diffusion (SD) finite element method for the one and one-half dimensional relativistic Vlasov-Maxwell system. The SD scheme yields a weak formulation, that corresponds to an…
The Inverse Problem for the estimation of a point-wise approximation error occurring at the discretization and solving of the system of partial differential equations is addressed. The set of the differences between the numerical solutions…
A general framework for goal-oriented a posteriori error estimation for finite volume methods is presented. The framework does not rely on recasting finite volume methods as special cases of finite element methods, but instead directly…