Related papers: A posteriori Error Estimates for Numerical Solutio…
This article describes the extension of recent methods for a posteriori error estimation such as dual-weighted residual methods to node-centered finite volume discretizations of second order elliptic boundary value problems including upwind…
This work presents a numerical study of functional type a posteriori error estimates for IgA approximation schemes in the context of elliptic boundary-value problems. Along with the detailed discussion of the most crucial properties of such…
An initial-boundary value problem of subdiffusion type is considered; the temporal component of the differential operator has the form $\sum_{i=1}^{\ell}q_i(t)\, D _t ^{\alpha_i} u(x,t)$, where the $q_i$ are continuous functions, each $D _t…
We consider a Markov chain approximation scheme for utility maximization problems in continuous time, which uses, in turn, a piecewise constant policy approximation, Euler-Maruyama time stepping, and a Gauss-Hermite approximation of the…
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…
This paper studies finite volume schemes for scalar hyperbolic conservation laws on evolving hypersurfaces of $\mathbb{R}^3$. We compare theoretical schemes assuming knowledge of all geometric quantities to (practical) schemes defined on…
We introduce stabilized spline collocation schemes for the numerical solution of nonlinear, hyperbolic conservation laws. A nonlinear, residual-based viscosity stabilization is combined with a projection stabilization-inspired linear…
We propose a novel model reduction approach for the approximation of non linear hyperbolic equations in the scalar and the system cases. The approach relies on an offline computation of a dictionary of solutions together with an online…
We consider finite element solutions to optimization problems, where the state depends on the possibly constrained control through a linear partial differential equation. Basing upon a reduced and rescaled optimality system, we derive a…
A posteriori estimates for mixed finite element discretizations of the Navier-Stokes equations are derived. We show that the task of estimating the error in the evolutionary Navier-Stokes equations can be reduced to the estimation of the…
The aim in model order reduction is to approximate an input-output map described by a large-scale dynamical system with a low-dimensional and cheaper-to-evaluate reduced order model. While high fidelity can be achieved by a variety of…
We present the first systematic work for deriving a posteriori error estimates for general non-polynomial basis functions in an interior penalty discontinuous Galerkin (DG) formulation for solving eigenvalue problems associated with second…
For the pure biharmonic equation and a biharmonic singular perturbation problem, a residual-based error estimator is introduced which applies to many existing nonconforming finite elements. The error estimator involves the local…
We derive optimal order a posteriori error estimates in the $L^\infty(L^2)$ and $L^1(L^2)$-norms for the fully discrete approximations of time fractional parabolic differential equations. For the discretization in time, we use the $L1$…
In this paper we present a family of high order cut finite element methods with bound preserving properties for hyperbolic conservation laws in one space dimension. The methods are based on the discontinuous Galerkin framework and use a…
In a general setting, we study a posteriori estimates used in finite element analysis to measure the error between a solution and its approximation. The latter is not necessarily generated by a finite element method. We show that the error…
The new concept of numerical smoothness is applied to RKDG methods on the scalar nonlinear conservation laws. The main result is an a posteriori error estimate for the RKDG methods of arbitrary order in space and time, with optimal…
In this article, we present an overview of different a posteriori error analysis and postprocessing methods proposed in the context of nonlinear eigenvalue problems, e.g. arising inelectronic structure calculations for the calculation of…
This work provides reliable a posteriori error estimates for Runge-Kutta discontinuous Galerkin approximations of nonlinear convection-diffusion systems. The classes of systems we study are quite general with a focus on convection-dominated…
We propose and analyze a posteriori error estimators for an optimal control problem that involves an elliptic partial differential equation as state equation and a control variable that enters the state equation as a coefficient; pointwise…