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In the present study, the efficiency of preconditioners for solving linear systems associated with the discretized variable-density incompressible Navier-Stokes equations with semiimplicit second-order accuracy in time and spectral accuracy…

In this work we examine a posteriori error control for post-processed approximations to elliptic boundary value problems. We introduce a class of post-processing operator that `tweaks' a wide variety of existing post-processing techniques…

Numerical Analysis · Mathematics 2023-03-01 Andreas Dedner , Jan Giesselmann , Tristan Pryer , Jennifer K Ryan

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

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 article, we derive \textit{a posteriori} error estimates for the Dirichlet boundary control problem governed by Stokes equation. An energy-based method has been deployed to solve the Dirichlet boundary control problem. We employ an…

Numerical Analysis · Mathematics 2024-01-30 Thirupathi Gudi , Ramesh Chandra Sau

We propose and analyze unfitted finite element approximations for the two-phase incompressible Navier--Stokes flow in an axisymmetric setting. The discretized schemes are based on an Eulerian weak formulation for the Navier--Stokes equation…

Numerical Analysis · Mathematics 2023-09-12 Harald Garcke , Robert Nürnberg , Quan Zhao

Numerical simulation of incompressible viscous flow, in particular in three space dimensions, continues to remain a challenging task. Space-time finite element methods feature the natural construction of higher order discretization schemes.…

Numerical Analysis · Mathematics 2022-10-07 Mathias Anselmann , Markus Bause

We present an a posteriori error analysis for one-dimensional random hyperbolic systems of conservation laws. For the discretization of the random space we consider the Non-Intrusive Spectral Projection method, the spatio-temporal…

Numerical Analysis · Mathematics 2019-08-27 Jan Giesselmann , Fabian Meyer , Christian Rohde

Numerical investigations of partial differential equations with hysteresis have largely focused on simulations, leaving numerical error analysis unexplored and relying mainly on derivative-free nonlinear solvers. This work establishes…

Numerical Analysis · Mathematics 2025-12-01 Shu Xu , Liqun Cao

The companion paper "Higher-order in time quasi-unconditionally stable ADI solvers for the compressible Navier-Stokes equations in 2D and 3D curvilinear domains", which is referred to as Part I in what follows, introduces ADI (Alternating…

Computational Physics · Physics 2018-01-11 Oscar Bruno , Max Cubillos

Finite element approximation to a decoupled formulation for the quad--curl problem is studied in this paper. The difficulty of constructing elements with certain conformity to the quad--curl problems has been greatly reduced. For convex…

Numerical Analysis · Mathematics 2021-12-09 Shuhao Cao , Long Chen , Xuehai Huang

This paper presents both a priori and a posteriori error analyses for a really pressure-robust virtual element method to approximate the incompressible Brinkman problem. We construct a divergence-preserving reconstruction operator using the…

Numerical Analysis · Mathematics 2024-12-02 Yu Xiong , Yanping Chen

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

In this paper, we introduce a fourth-order accurate finite element method for incompressible variable density flow. The method is implicit in time and constructed with the Taylor series technique, and uses standard high-order Lagrange basis…

Numerical Analysis · Mathematics 2022-09-21 Lukas Lundgren , Murtazo Nazarov

We derive energy-norm a posteriori error bounds for an Euler time-stepping method combined with various spatial discontinuous Galerkin schemes for linear parabolic problems. For accessibility, we address first the spatially semidiscrete…

Numerical Analysis · Mathematics 2011-04-06 Emmanuil H. Georgoulis , Omar Lakkis , Juha M. Virtanen

A novel reduced-order model for nonlinear flows is presented. The model arises from a resolvent decomposition in which the nonlinear advection terms of the Navier-Stokes equation are considered as the input to a linear system in Fourier…

Fluid Dynamics · Physics 2016-06-16 F Gómez , HM Blackburn , M Rudman , AS Sharma , BJ McKeon

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…

Numerical Analysis · Mathematics 2017-09-08 Andreas Dedner , Jan Giesselmann

This paper describes a new multilevel procedure that can solve the discrete Navier-Stokes system arising from finite volume discretizations on composite grids, which may consist of more than one level. SIMPLE is used and tested as the…

Computational Physics · Physics 2015-08-14 Alexandros Syrakos , Apostolos Goulas

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 $L1$…

Numerical Analysis · Mathematics 2023-11-14 Jiliang Cao , Wansheng Wang , Aiguo Xiao

The present paper addresses the numerical solution of turbulent flows with high-order discontinuous Galerkin methods for discretizing the incompressible Navier-Stokes equations. The efficiency of high-order methods when applied to…

Fluid Dynamics · Physics 2018-08-29 Niklas Fehn , Wolfgang A. Wall , Martin Kronbichler