A posteriori error estimation and adaptive mesh refinement for a multiscale operator decomposition approach to fluid-solid heat transfer

DOI10.1016/j.jcp.2010.02.003zbMath1281.80004OpenAlexW2049665751MaRDI QIDQ974291

Tim Wildey, Simon J. Tavener, Donald J. Estep

Publication date: 27 May 2010

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2010.02.003

zbMATH Keywords

finite element methodadaptive mesh refinementconjugate heat transferGreens functionsa posteriori error analysismultiscale methodsadjoint problemflux recoveryoperator decompositionboundary flux correctionmulti-discretization methods

Mathematics Subject Classification ID

Incompressible viscous fluids (76D99) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer (80M10)

Related Items

The interaction of iteration error and stability for linear partial differential equations coupled through an interface ⋮ Analysis and application of high order implicit Runge-Kutta schemes for unsteady conjugate heat transfer: a strongly-coupled approach ⋮ Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates ⋮ A Posteriori Analysis and Efficient Refinement Strategies for the Poisson--Boltzmann Equation ⋮ A Posteriori Error Estimates for Mixed Finite Element and Finite Volume Methods for Parabolic Problems Coupled through a Boundary ⋮ High resolution sharp computational methods for elliptic and parabolic problems in complex geometries ⋮ Quantification of errors for operator-split advection-diffusion calculations ⋮ \textit{A posteriori} analysis of an iterative multi-discretization method for reaction-diffusion systems ⋮ Towards efficient backward-in-time adjoint computations using data compression techniques ⋮ A posteriori analysis of a multirate numerical method for ordinary differential equations ⋮ Monolithic discretization of linear thermoelasticity problems via adaptive multimesh \(hp\)-FEM ⋮ A sharp computational method for the simulation of the solidification of binary alloys

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Approximate boundary-flux calculations
• Derivative calculation from finite element solutions
• Galerkin approximations for the two point boundary problem using continuous, piecewise polynomial spaces
• Generic solvability of the axisymmetric 3-D Euler equations and the 2-D Boussinesq equations
• Global well-posedness of the viscous Boussinesq equations
• Interface relaxation methods for elliptic differential equations
• A posteriori analysis and adaptive error control for operator decomposition solution of coupled semilinear elliptic systems
• A Posteriori Analysis and Improved Accuracy for an Operator Decomposition Solution of a Conjugate Heat Transfer Problem
• An optimal control approach to a posteriori error estimation in finite element methods
• Adaptive finite element approximation of coupled flow and transport problems with applications in heat transfer
• A posteriori error estimation of approximate boundary fluxes
• Adaptive finite element approximation of multiphysics problems
• An A Posteriori–A Priori Analysis of Multiscale Operator Splitting
• Local existence and blow-up criterion of Hölder continuous solutions of the Boussinesq equations
• A Posteriori Error Bounds and Global Error Control for Approximation of Ordinary Differential Equations
• Stability analysis of numerical interface conditions in fluid-structure thermal analysis
• Duality-based adaptivity in the hp-finite element method
• Estimating the error of numerical solutions of systems of reaction-diffusion equations
• The Construction of Preconditioners for Elliptic Problems by Substructuring. I
• Iterative Methods for the Solution of Elliptic Problems on Regions Partitioned into Substructures
• Bifurcation for flow past a cylinder between parallel planes
• A parallel iterative nonoverlapping domain decomposition procedure for elliptic problems
• A Posteriori Analysis and Adaptive Error Control for Multiscale Operator Decomposition Solution of Elliptic Systems I: Triangular Systems
• Generalized Green's Functions and the Effective Domain of Influence
• Equivalent Norms for Sobolev Spaces