Related papers: A posteriori error estimates for leap-frog and cos…
We consider some (anisotropic and piecewise constant) convection-diffusion-reaction problems in domains of R2, approximated by a discontinuous Galerkin method with polynomials of any degree. We propose two a posteriori error estimators…
In this paper, a backward Euler method combined with finite element discretization in spatial direction is discussed for the equations of motion arising in the $2D$ Oldroyd model of viscoelastic fluids of order one with the forcing term…
We derive a posteriori error estimates in the $L_\infty((0,T];L_\infty(\Omega))$ norm for approximations of solutions to linear para bolic equations. Using the elliptic reconstruction technique introduced by Makridakis and Nochetto and heat…
We consider second-order evolution equations in an abstract setting with damping and time delay and give sufficient conditions ensuring exponential stability. Our abstract framework is then applied to the wave equation, the elasticity…
The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled employing the fixed-stress…
We develop and implement a novel fast bootstrap for dependent data. Our scheme is based on the i.i.d. resampling of the smoothed moment indicators. We characterize the class of parametric and semi-parametric estimation problems for which…
Nowadays, a posteriori error control methods have formed a new important part of the numerical analysis. Their purpose is to obtain computable error estimates in various norms and error indicators that show distributions of global and local…
We consider a second order linear evolution equation with a dissipative term multiplied by a time-dependent coefficient. Our aim is to design the coefficient in such a way that all solutions decay in time as fast as possible. We discover…
We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler scheme in time and the Gradient Discretisation method in…
We present reliable a posteriori estimators for some fully discrete schemes applied to nonlinear systems of hyperbolic conservation laws in one space dimension with strictly convex entropy. The schemes are based on a method of lines…
We consider systems of ordinary differential equations with multiple scales in time. In general, we are interested in the long time horizon of a slow variable that is coupled to solution components that act on a fast scale. Although the…
A nonlinear adaptive procedure for optimising both the schemes in time and space is proposed in view of increasing the numerical efficiency and reducing the computational time. The method is based on a four-parameter family of schemes we…
The numerical analysis of time fractional evolution equations with the second-order elliptic operator including general time-space dependent variable coefficients is challenging, especially when the classical weak initial singularities are…
A class of linear parabolic equations is considered. We derive a framework for the a posteriori error analysis of time discretisations by Richardson extrapolation of arbitrary order combined with finite element discretisations in space. We…
This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian…
In this note we shall devise a variable-order continuous Galerkin time stepping method which is especially geared towards norm-preserving dynamical systems. In addition, we will provide an a posteriori estimate for the $L^\infty$-error.
We propose and analyze a reliable and efficient a posteriori error estimator for the pointwise tracking optimal control problem of the Stokes equations. This linear-quadratic optimal control problem entails the minimization of a cost…
Motivated by problems in contact mechanics, we propose a duality approach for computing approximations and associated a posteriori error bounds to solutions of variational inequalities of the first kind. The proposed approach improves upon…
This work presents the multiharmonic analysis and derivation of functional type a posteriori estimates of a distributed eddy current optimal control problem and its state equation in a time-periodic setting. The existence and uniqueness of…
We provide rigorous and computable a-posteriori error estimates for first order finite-volume approximations of nonlinear systems of hyperbolic conservation laws in one spatial dimension. Our estimators rely on recent stability results by…