The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform
Lina Song - One of the best experts on this subject based on the ideXlab platform.
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Recovery-Based Error Estimator for Stabilized Finite Element Method for the Stationary Navier--Stokes Problem
SIAM Journal on Scientific Computing, 2016Co-Authors: Lina Song, Haiyan Su, Xinlong FengAbstract:A recovery-Based Error Estimator is proposed and analyzed for stabilized $P_1/P_0$ (continuous linear velocity/constant pressure) finite element approximations to the stationary Navier--Stokes problem. We establish the reliability and efficiency of the Error Estimator. A crucial part of this work is the estimation for the nonlinear term of the Navier--Stokes problem. It turns out such a term can be bounded by the recovery-Based Error Estimator. Numerical results are provided to illustrate the performance of the Error Estimator.
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Recovery-Based Error Estimator for stabilized finite element methods for the stationary Navier-Stokes problem
2016Co-Authors: Lina SongAbstract:A recovery-Based Error Estimator is proposed and analyzed for stabilized $P_1/P_0$ (continuous linear velocity/constant pressure) finite element approximations to the stationary Navier-Stokes problem. We establish the reliability and efficiency of the Error Estimator. A crucial part of this work is the estimation for the nonlinear term of the Navier-Stokes problem. It turns out such term can be bounded by the recovery-Based Error Estimator. Numerical results are provided to illustrate the performance of the Error Estimator.
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recovery Based Error Estimator for stabilized finite element methods for the stokes equation
Computer Methods in Applied Mechanics and Engineering, 2014Co-Authors: Lina SongAbstract:Abstract A recovery-Based Error Estimator is proposed and analyzed for stabilized P 1 / P 0 (continuous linear velocity/constant pressure) finite element approximations to the Stokes equation. Reliability and efficiency of the Estimator are established for various stabilized methods. For several test problems, numerical results show that our Estimator is more accurate than the classical residual Error Estimator.
Yerlan Amanbek - One of the best experts on this subject based on the ideXlab platform.
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Error indicators for incompressible darcy flow problems using enhanced velocity mixed finite element method
Computer Methods in Applied Mechanics and Engineering, 2020Co-Authors: Yerlan Amanbek, Gurpreet Singh, Gergina Pencheva, Mary F. WheelerAbstract:Abstract Local mesh adaptivity serves as a practical tool in numerical simulations to accurately capture features of interest while reducing computational time and memory requirements. In this work, we suggest a refinement strategy Based on pressure and flux Error estimates for numerical simulation of an incompressible, single phase flow and transport process in the subsurface porous media. We derive a posteriori Error estimates for an Enhanced Velocity Mixed Finite Element Method (EVMFEM) as a spatial domain decomposition approach. We note that the flux Errors play an important role in coupled flow and transport systems later demonstrated using numerical experiments. A comparison between explicit (residual Based) Error Estimators and an implicit Error Estimator; Based upon the post-processing proposed by Arbogast and Chen (1995), shows that the latter performs better. A residual-Based Error Estimator for pressure was found to be both computationally efficient while sufficiently indicating the large Error subdomains. Numerical studies are also presented that confirm our theoretical derivations while demonstrating the advantages of post-processing in detecting velocity Errors.
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Error indicator for the incompressible darcy flow problems using enhanced velocity mixed finite element method
arXiv: Numerical Analysis, 2019Co-Authors: Yerlan Amanbek, Gurpreet Singh, Gergina Pencheva, Mary F. WheelerAbstract:In the flow and transport numerical simulation, mesh adaptivity strategy is important in reducing the usage of CPU time and memory. The refinement Based on the pressure Error Estimator is commonly-used approach without considering the flux Error which plays important role in coupling flow and transport systems. We derive a posteriori Error Estimators for Enhanced Velocity Mixed Finite Element Method (EVMFEM) in the incompressible Darcy flow. We show numerically difference of the explicit residual Based Error Estimator and implicit Error Estimators, where Arbogast and Chen post-processing procedure from [1] for pressure was used to improve Estimators. A residual-Based Error Estimator provides a better indicator for pressure Error. Proposed Estimators are good indicators in finding of the large Error element. Numerical tests confirm theoretical results. We show the advantage of pressure postprocessing on the detecting of velocity Error. To the authors' best knowledge, a posteriori Error analysis of EVMFEM has been scarcely investigated from the theoretical and numerical point of view. Reference. 1. Arbogast, T., & Chen, Z. (1995). On the implementation of mixed methods as nonconforming methods for second-order elliptic problems. Mathematics of Computation, 64(211), 943-972.
David L Darmofal - One of the best experts on this subject based on the ideXlab platform.
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a triangular cut cell adaptive method for high order discretizations of the compressible navier stokes equations
Journal of Computational Physics, 2007Co-Authors: Krzysztof J Fidkowski, David L DarmofalAbstract:This paper presents a mesh adaptation method for higher-order (p>1) discontinuous Galerkin (DG) discretizations of the two-dimensional, compressible Navier-Stokes equations. A key feature of this method is a cut-cell meshing technique, in which the triangles are not required to conform to the boundary. This approach permits anisotropic adaptation without the difficulty of constructing meshes that conform to potentially complex geometries. A quadrature technique is proposed for accurately integrating on general cut cells. In addition, an output-Based Error Estimator and adaptive method are presented, appropriately accounting for high-order solution spaces in optimizing local mesh anisotropy. Accuracy on cut-cell meshes is demonstrated by comparing solutions to those on standard, boundary-conforming meshes. Robustness of the cut-cell and adaptation technique is successfully tested for highly anisotropic boundary-layer meshes representative of practical high Re simulations. Furthermore, adaptation results show that, for all test cases considered, p=2 and p=3 discretizations meet desired Error tolerances using fewer degrees of freedom than p=1.
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output Based adaptive meshing using triangular cut cells
2006Co-Authors: Krzysztof J Fidkowski, David L DarmofalAbstract:This report presents a mesh adaptation method for higher-order (p > 1) discontinuous Galerkin (DG) discretizations of the two-dimensional, compressible Navier-Stokes equations. The method uses a mesh of triangular elements that are not required to conform to the boundary. This triangular, cut-cell approach permits anisotropic adaptation without the difficulty of constructing meshes that conform to potentially complex geometries. A quadrature technique is presented for accurately integrating on general cut cells. In addition, an output-Based Error Estimator and adaptive method are presented, with emphasis on appropriately accounting for high-order solution spaces in optimizing local mesh anisotropy. Accuracy on cut-cell meshes is demonstrated by comparing solutions to those on standard boundary-conforming meshes. Adaptation results show that, for all test cases considered, p = 2 and p = 3 discretizations meet desired Error tolerances using fewer degrees of freedom than p = 1. Furthermore, an initial-mesh dependence study demonstrates that, for sufficiently low Error tolerances, the final adapted mesh is relatively insensitive to the starting mesh. An abbreviated version of this report was submitted to the Journal of Computational Physics. Department Of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139 (kfid@mit.edu, darmofal@mit.edu).
Mary F. Wheeler - One of the best experts on this subject based on the ideXlab platform.
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Error indicators for incompressible darcy flow problems using enhanced velocity mixed finite element method
Computer Methods in Applied Mechanics and Engineering, 2020Co-Authors: Yerlan Amanbek, Gurpreet Singh, Gergina Pencheva, Mary F. WheelerAbstract:Abstract Local mesh adaptivity serves as a practical tool in numerical simulations to accurately capture features of interest while reducing computational time and memory requirements. In this work, we suggest a refinement strategy Based on pressure and flux Error estimates for numerical simulation of an incompressible, single phase flow and transport process in the subsurface porous media. We derive a posteriori Error estimates for an Enhanced Velocity Mixed Finite Element Method (EVMFEM) as a spatial domain decomposition approach. We note that the flux Errors play an important role in coupled flow and transport systems later demonstrated using numerical experiments. A comparison between explicit (residual Based) Error Estimators and an implicit Error Estimator; Based upon the post-processing proposed by Arbogast and Chen (1995), shows that the latter performs better. A residual-Based Error Estimator for pressure was found to be both computationally efficient while sufficiently indicating the large Error subdomains. Numerical studies are also presented that confirm our theoretical derivations while demonstrating the advantages of post-processing in detecting velocity Errors.
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Error indicator for the incompressible darcy flow problems using enhanced velocity mixed finite element method
arXiv: Numerical Analysis, 2019Co-Authors: Yerlan Amanbek, Gurpreet Singh, Gergina Pencheva, Mary F. WheelerAbstract:In the flow and transport numerical simulation, mesh adaptivity strategy is important in reducing the usage of CPU time and memory. The refinement Based on the pressure Error Estimator is commonly-used approach without considering the flux Error which plays important role in coupling flow and transport systems. We derive a posteriori Error Estimators for Enhanced Velocity Mixed Finite Element Method (EVMFEM) in the incompressible Darcy flow. We show numerically difference of the explicit residual Based Error Estimator and implicit Error Estimators, where Arbogast and Chen post-processing procedure from [1] for pressure was used to improve Estimators. A residual-Based Error Estimator provides a better indicator for pressure Error. Proposed Estimators are good indicators in finding of the large Error element. Numerical tests confirm theoretical results. We show the advantage of pressure postprocessing on the detecting of velocity Error. To the authors' best knowledge, a posteriori Error analysis of EVMFEM has been scarcely investigated from the theoretical and numerical point of view. Reference. 1. Arbogast, T., & Chen, Z. (1995). On the implementation of mixed methods as nonconforming methods for second-order elliptic problems. Mathematics of Computation, 64(211), 943-972.
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a domain decomposition approach for local mesh refinement in space and time
arXiv: Numerical Analysis, 2018Co-Authors: Gurpreet Singh, Mary F. WheelerAbstract:We present an adaptive space-time mesh refinement approach Based a domain decomposition approach (Singh and Wheeler, 2018) that allows different time-step sizes and mesh refinements in different subdomains. Our numerical experiments indicate that non-linear solvers fail to converge, to the desired tolerance, due to large non-linear residuals in a smaller subdomain. We exploit this feature to identify subdomains where smaller time-step sizes are necessary while using large time-step sizes in the rest of the reservoir domain. The three key components of our approach are: (1) a space-time, enhanced velocity, domain decomposition approach that allows different mesh refinements and time-step sizes in different subdomains while preserving local mass conservation, (2) a residual Based Error Estimator to identify or mark regions (or subdomains) that pose non-linear convergence issues, and (3) a fully coupled monolithic solver is also presented that solves the coarse and fine subdomain problems, both in space and time, simultaneously. This solution scheme is fully implicit and is therefore unconditionally stable. The proposed space-time domain decomposition approach, with smaller time-step sizes in a subdomain and large time-step sizes everywhere else, circumvents the non-linear convergence issue without adding computational costs. Additionally, a space-time monolithic solver renders a massively parallel, time concurrent framework for solving flow and transport problems in subsurface porous media. Since the proposed approach is similar to the widely used finite difference scheme, it can be easily integrated in any existing legacy reservoir simulator.
A Borio - One of the best experts on this subject based on the ideXlab platform.
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A residual a posteriori Error estimate for the Virtual Element Method
Mathematical Models and Methods in Applied Sciences, 2017Co-Authors: S Berrone, A BorioAbstract:A residual-Based a posteriori Error estimate for the Poisson problem with discontinuous diffusivity coefficient is derived in the case of a virtual element discretization. The Error is measured considering a suitable polynomial projection of the discrete solution to prove an equivalence between the defined Error and a computable residual Based Error Estimator that does not involve any term related to the virtual element stabilization. Numerical results display a very good behavior of the ratio between the Error and the Error Estimator, resulting independent of the meshsize and element distortion.