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A posteriori error estimator is derived for an elliptic interface problem in the fictitious domain formulation with distributed Lagrange multiplier considering a discontinuous Lagrange multiplier finite element space. A posteriori error…

Numerical Analysis · Mathematics 2024-07-02 Najwa Alshehri , Daniele Boffi , Lucia Gastaldi

In this paper we consider a sub-diffusion problem where the fractional time derivative is approximated either by the L1 scheme or by Convolution Quadrature. We propose new interpretations of the numerical schemes which lead to a posteriori…

Numerical Analysis · Mathematics 2022-03-02 Lehel Banjai , Charalambos G. Makridakis

We derive a residual based a-posteriori error estimate for the outer normal flux of approximations to {the diffusion problem with variable coefficient}. By analyzing the solution of the adjoint problem, we show that error indicators in the…

Numerical Analysis · Mathematics 2021-10-26 Silvia Bertoluzza , Erik Burman , Cuiyu He

We revisit the L2 norm error estimate for the C0 interior penalty analysis of fourth order Dirichlet boundary control problem. The L2 norm estimate for the optimal control is derived under reduced regularity assumption and this analysis can…

Optimization and Control · Mathematics 2022-10-18 Sudipto Chowdhury , Divay Garg , Ravina Shokeen

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…

Numerical Analysis · Mathematics 2020-07-07 Jehanzeb H. Chaudhry , J. B. Collins

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…

Numerical Analysis · Mathematics 2021-11-16 Johannes Kraus , Sergey Repin

This paper is concerned with the recovery of (approximate) solutions to parabolic problems from incomplete and possibly inconsistent observational data, given on a time-space cylinder that is a strict subset of the computational domain…

Numerical Analysis · Mathematics 2021-07-13 Wolfgang Dahmen , Rob Stevenson , Jan Westerdiep

In this paper, we consider the integrating factor midpoint method for wave-type equations and derive optimal order a posteriori error estimates. We first introduce an integrating factor midpoint approximation defined by the piecewise linear…

Numerical Analysis · Mathematics 2026-03-03 Xianfa Hu , Fazhan Geng , Wansheng Wang

This work deals with the a posteriori error estimates for the Darcy-Forchheimer problem. We introduce the corresponding variational formulation and discretize it by using the finite-element method. A posteriori error estimate with two types…

Numerical Analysis · Mathematics 2022-02-24 Georges Semaan , Toni Sayah , Faouzi Triki

We design and analyze a posteriori error estimators for the Stokes system with singular sources in suitable $\mathbf{W}^{1,p}\times \mathrm{L}^p$ spaces. We consider classical low-order inf-sup stable and stabilized finite element…

Numerical Analysis · Mathematics 2019-12-19 Francisco Fuica , Felipe Lepe , Enrique Otarola , Daniel Quero

This work reviews goal-oriented a posteriori error control, adaptivity and solver control for finite element approximations to boundary and initial-boundary value problems for stationary and non-stationary partial differential equations,…

Numerical Analysis · Mathematics 2024-12-02 Bernhard Endtmayer , Ulrich Langer , Thomas Richter , Andreas Schafelner , Thomas Wick

We consider a 1D periodic atomistic model, for which we formulate and analyze an adaptive variant of a quasicontinuum method. We establish a posteriori error estimates for the energy norm and for the energy, based on a posteriori residual…

Numerical Analysis · Mathematics 2017-02-15 Christoph Ortner , Hao Wang

We devise a posteriori error estimators for quasi-optimal nonconforming finite element methods approximating symmetric elliptic problems of second and fourth order. These estimators are defined for all source terms that are admissible to…

Numerical Analysis · Mathematics 2025-02-05 Christian Kreuzer , Matthias Rott , Andreas Veeser , Pietro Zanotti

In this paper, the optimal strong error estimates for stochastic parabolic optimal control problem with additive noise and integral state constraint are derived based on time-implicit and finite element discretization. The continuous and…

Optimization and Control · Mathematics 2025-05-13 Qiming Wang , Wanfang Shen , Wenbin Liu

We provide a posteriori error estimates for a discontinuous Galerkin scheme for the parabolic-elliptic Keller-Segel system in 2 or 3 space dimensions. The estimates are conditional, in the sense that an a posteriori computable quantity…

Numerical Analysis · Mathematics 2024-06-12 Jan Giesselmann , Kiwoong Kwon

We propose a novel a posteriori error estimator for the N\'ed\'elec finite element discretization of time-harmonic Maxwell's equations. After the approximation of the electric field is computed, we propose a fully localized algorithm to…

Numerical Analysis · Mathematics 2024-02-28 T. Chaumont-Frelet

The aim of this work is to derive a priori error estimates for finite element discretizations of control--constrained optimal control problems that involve the Stokes system and Dirac measures. The first problem entails the minimization of…

Numerical Analysis · Mathematics 2020-04-29 Francisco Fuica , Enrique Otarola , Daniel Quero

In this paper we study an a posteriori error indicator introduced in E. Dari, R.G. Duran, C. Padra, Appl. Numer. Math., 2012, for the approximation of the Laplace eigenvalue problem with Crouzeix-Raviart non-conforming finite elements. In…

Numerical Analysis · Mathematics 2014-11-11 Daniele Boffi , Ricardo G. Durán , Francesca Gardini , Lucia Gastaldi

In this work, new theoretical results on functional type a posteriori estimates for elliptic optimal control problems with control constraints are presented. More precisely, we derive new, sharp, guaranteed and fully computable lower bounds…

Optimization and Control · Mathematics 2015-06-02 Monika Wolfmayr

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…

Numerical Analysis · Mathematics 2015-03-26 Shaohong Du , Xiaoping Xie