A review and comparison of error estimators for anisotropic mesh adaptation for flow simulations
Automated mesh adaptation is known to be an efficient way to control discretization errors in
Computational Fluid Dynamics (CFD) simulations. It offers the added advantage that the …
Computational Fluid Dynamics (CFD) simulations. It offers the added advantage that the …
Goal-oriented mesh adaptation method for nonlinear problems including algebraic errors
V Dolejší, O Bartoš, F Roskovec - Computers & Mathematics with …, 2021 - Elsevier
We deal with the goal-oriented error estimates and mesh adaptation for nonlinear partial
differential equations. The setting of the adjoint problem and the resulting estimates are not …
differential equations. The setting of the adjoint problem and the resulting estimates are not …
[HTML][HTML] Goal-oriented a posteriori error estimation for conforming and nonconforming approximations with inexact solvers
We derive a unified framework for goal-oriented a posteriori estimation covering in particular
higher-order conforming, nonconforming, and discontinuous Galerkin finite element …
higher-order conforming, nonconforming, and discontinuous Galerkin finite element …
Adjoint-based anisotropic hp-adaptation for discontinuous Galerkin methods using a continuous mesh model
A Rangarajan, G May, V Dolejsi - Journal of Computational Physics, 2020 - Elsevier
In this paper we propose an adjoint-based hp-adaptation method for conservation laws, and
corresponding numerical schemes based on piecewise polynomial approximation spaces …
corresponding numerical schemes based on piecewise polynomial approximation spaces …
[图书][B] Anisotropic hp-Mesh Adaptation Methods
V Dolejší, G May - 2022 - Springer
Partial differential equations (PDE) govern many problems of scientific and engineering
interest. Consequently, numerical solution of PDE has become a key technology in the …
interest. Consequently, numerical solution of PDE has become a key technology in the …
[HTML][HTML] An Anisotropic hp-mesh Adaptation Method for Time-Dependent Problems Based on Interpolation Error Control
V Dolejší, G May - Journal of Scientific Computing, 2023 - Springer
We propose an efficient mesh adaptive method for the numerical solution of time-dependent
partial differential equations considered in the fixed space-time cylinder Ω×(0, T). We employ …
partial differential equations considered in the fixed space-time cylinder Ω×(0, T). We employ …
[HTML][HTML] A goal-oriented anisotropic hp-mesh adaptation method for linear convection–diffusion–reaction problems
O Bartoš, V Dolejší, G May, A Rangarajan… - … & Mathematics with …, 2019 - Elsevier
We deal with the numerical solution of linear convection–diffusion–reaction equations using
the h p-variant of the discontinuous Galerkin method on triangular grids. We develop a mesh …
the h p-variant of the discontinuous Galerkin method on triangular grids. We develop a mesh …
An adjoint-based adaptive error approximation of functionals by the hybridizable discontinuous Galerkin method for second-order elliptic equations
B Cockburn, S Xia - Journal of Computational Physics, 2022 - Elsevier
This paper presents a novel, fully computable error approximation and mesh adaptation
approach for functionals defined by second-order elliptic equations. The functionals are …
approach for functionals defined by second-order elliptic equations. The functionals are …
An anisotropic h-adaptive strategy for discontinuous Petrov-Galerkin schemes using a continuous mesh model
A Chakraborty, AM Rangarajan, G May - Computers & Mathematics with …, 2022 - Elsevier
Abstract Certain Petrov-Galerkin schemes deliver inherently stable formulations of
variational problems on a given mesh by selecting appropriate pairs of trial and test spaces …
variational problems on a given mesh by selecting appropriate pairs of trial and test spaces …
Goal-oriented error estimation and mesh adaptation for tracer transport modelling
This paper applies metric-based mesh adaptation methods to advection-dominated tracer
transport modelling problems in two and three dimensions, using the finite element package …
transport modelling problems in two and three dimensions, using the finite element package …