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The numerical approximation of convection-dominated problems continues to remain subject of strong interest. Families of stabilization techniques for finite element methods were developed in the past. Adaptive techniques based on a…

Numerical Analysis · Mathematics 2018-03-20 Kristina Schwegler , Marius P. Bruchhäuser , Markus Bause

We construct a space-time parallel method for solving parabolic partial differential equations by coupling the Parareal algorithm in time with overlapping domain decomposition in space. The goal is to obtain a discretization consisting of…

Numerical Analysis · Mathematics 2022-01-17 Jehanzeb Chaudhry , Donald Estep , Simon Tavener

We derive a posteriori error estimators for an optimal control problem governed by a convection-reaction-diffusion equation; control constraints are also considered. We consider a family of low-order stabilized finite element methods to…

Numerical Analysis · Mathematics 2017-04-24 Alejandro Allendes , Enrique Otarola , Richard Rankin

We study a posteriori error analysis of linear-quadratic boundary control problems under bilateral box constraints on the control which acts through a Neumann type boundary condition. We adopt the hybridizable discontinuous Galerkin method…

Numerical Analysis · Mathematics 2020-04-21 Haitao Leng , Yanping Chen

This work derives a residual-based a posteriori error estimator for reduced models learned with non-intrusive model reduction from data of high-dimensional systems governed by linear parabolic partial differential equations with control…

Numerical Analysis · Mathematics 2020-05-13 Wayne Isaac Tan Uy , Benjamin Peherstorfer

This work is devoted to the study of a posteriori error estimation and adaptivity in parabolic problems with a particular focus on spatial discontinuous Galerkin (dG) discretisations. We begin by deriving an a posteriori error estimator for…

Numerical Analysis · Mathematics 2015-04-13 Stephen Arthur Metcalfe

The paper is concerned with parabolic time-periodic boundary value problems which are of theoretical interest and arise in different practical applications. The multiharmonic finite element method is well adapted to this class of parabolic…

Numerical Analysis · Mathematics 2014-11-12 Ulrich Langer , Sergey Repin , Monika Wolfmayr

This paper introduces a novel a posteriori error estimation framework for the enriched Galerkin (EG) finite element method applied to linear parabolic equations. While the EG method has been recognized for its local conservation property…

Numerical Analysis · Mathematics 2026-04-29 Hyun-Geun Shin , Yi-Yung Yang , Sanghyun Lee

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…

Numerical Analysis · Computer Science 2018-05-28 Svetlana Matculevich

This paper develops and discusses a residual-based a posteriori error estimator for parabolic surface partial differential equations on closed stationary surfaces. The full discretization uses the surface finite element method in space and…

Numerical Analysis · Mathematics 2026-03-31 Balázs Kovács , Michael Lantelme

In this work, we further develop multigoal-oriented a posteriori error estimation with two objectives in mind. First, we formulate goal-oriented mesh adaptivity for multiple functionals of interest for nonlinear problems in which both the…

Numerical Analysis · Mathematics 2018-04-05 B. Endtmayer , U. Langer , T. Wick

In this paper, with the parametric symmetric coercive elliptic boundary value problem as an example of the primal-dual variational problems satisfying the strong duality, we develop primal-dual reduced basis methods (PD-RBM) with robust…

Numerical Analysis · Mathematics 2020-09-18 Shun Zhang

An a posteriori error bound for the pointwise error of the quadratic discontinuous Galerkin method for the unilateral contact problem on polygonal domain is presented. The pointwise a posteriori error analysis is based on the direct use of…

Numerical Analysis · Mathematics 2024-01-05 Rohit Khandelwal , Kamana Porwal , Tanvi Wadhawan

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

Regressions created from experimental or simulated data enable the construction of metamodels, widely used in a variety of engineering applications. Many engineering problems involve multi-parametric physics whose corresponding…

Computational Engineering, Finance, and Science · Computer Science 2021-03-10 Abel Sancarlos , Victor Champaney , Jean-Louis Duval , Elias Cueto , Francisco Chinesta

This paper is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of…

Optimization and Control · Mathematics 2015-11-19 Ulrich Langer , Sergey Repin , Monika Wolfmayr

Recovery type a posteriori error estimators are popular, particularly in the engineering community, for their computationally inexpensive, easy to implement, and generally asymptotically exactness. Unlike the residual type error estimators,…

Numerical Analysis · Mathematics 2025-03-26 Ying Liu , Jingjing Xiao , Nianyu Yi , Huihui Cao

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

Adaptive atomistic/continuum (a/c) coupling method is an important method for the simulation of material and atomistic systems with defects to achieve the balance of accuracy and efficiency. Residual based a posteriori error estimator is…

Numerical Analysis · Mathematics 2022-11-28 Yangshuai Wang , Hao Wang

This work is concerned with the derivation of a robust a posteriori error estimator for a discontinuous Galerkin method discretisation of linear non-stationary convection-diffusion initial/boundary value problems and with the implementation…

Numerical Analysis · Mathematics 2012-11-16 Andrea Cangiani , Emmanuil H. Georgoulis , Stephen Metcalfe