Goal-oriented mesh adaptation method for nonlinear problems including algebraic errors
From MaRDI portal
Publication:2027589
DOI10.1016/j.camwa.2021.04.004OpenAlexW3164341282MaRDI QIDQ2027589
Ondřej Bartoš, Filip Roskovec, Vít Dolejší
Publication date: 27 May 2021
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2021.04.004
Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)
Related Items
Rate-optimal goal-oriented adaptive FEM for semilinear elliptic PDEs ⋮ Goal-oriented error estimation based on equilibrated flux and potential reconstruction for the approximation of elliptic and parabolic problems ⋮ Goal-oriented error analysis of iterative Galerkin discretizations for nonlinear problems including linearization and algebraic errors ⋮ An anisotropic \textit{hp}-mesh adaptation method for time-dependent problems based on interpolation error control
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Efficient solution strategy for the semi-implicit discontinuous Galerkin discretization of the Navier-Stokes equations
- An adaptive Newton algorithm for optimal control problems with application to optimal electrode design
- Iterative Galerkin discretizations for strongly monotone problems
- The p- and h-p versions of the finite element method. An overview
- Fully anisotropic goal-oriented mesh adaptation for 3D steady Euler equations
- A fully automatic \(hp\)-adaptivity
- Residual based error estimates for the space-time discontinuous Galerkin method applied to the compressible flows
- Adjoint-based \textit{hp}-adaptivity on anisotropic meshes for high-order compressible flow simulations
- Adaptive error control for multigrid finite element methods
- Adaptive higher-order space-time discontinuous Galerkin method for the computer simulation of variably-saturated porous media flows
- A goal-oriented error estimator for a class of homogenization problems
- On the convergence of adaptive iterative linearized Galerkin methods
- A goal-oriented anisotropic \(hp\)-mesh adaptation method for linear convection-diffusion-reaction problems
- On efficient numerical solution of linear algebraic systems arising in goal-oriented error estimates
- Dual weighted residual error estimation for the finite cell method
- Goal-oriented a posteriori error estimation for conforming and nonconforming approximations with inexact solvers
- Computable error estimators for the approximation of nonlinear problems by linearized models
- Adaptive Inexact Newton Methods with A Posteriori Stopping Criteria for Nonlinear Diffusion PDEs
- Interplay between discretization and algebraic computation in adaptive numerical solutionof elliptic PDE problems
- On Efficient Numerical Approximation of the Bilinear Form $c^*A^{-1}b$
- Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality
- An optimal control approach to a posteriori error estimation in finite element methods
- Analysis of a Multilevel Iterative Method for Nonlinear Finite Element Equations
- Adaptive Discontinuous Galerkin Finite Element Methods for Nonlinear Hyperbolic Conservation Laws
- Rate optimal adaptive FEM with inexact solver for nonlinear operators
- Adaptive finite element analysis of nonlinear problems: balancing of discretization and iteration errors
- A design of residual error estimates for a high order BDF‐DGFE method applied to compressible flows
- Two-Side a Posteriori Error Estimates for the Dual-Weighted Residual Method
- A Goal-Oriented High-Order Anisotropic Mesh Adaptation Using Discontinuous Galerkin Method for Linear Convection-Diffusion-Reaction Problems
- Adaptive Optimal Control of the Obstacle Problem
- Discontinuous Galerkin Method
- The Role of the Jacobian in the Adaptive Discontinuous Galerkin Method for the Compressible Euler Equations
- Adjoint Consistency Analysis of Discontinuous Galerkin Discretizations
- Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: the scalar case
