A posteriori error analysis for a transient conjugate heat transfer problem

Article history: Received 2 September 2008 Accepted 13 October 2008 Available online 24 December 2008 MSC: 65N15 65N30 65N50

[1]  John N. Shadid,et al.  Stability of operator splitting methods for systems with indefinite operators: reaction-diffusion systems , 2005 .

[2]  Tim Wildey,et al.  A Posteriori Analysis and Improved Accuracy for an Operator Decomposition Solution of a Conjugate Heat Transfer Problem , 2008, SIAM J. Numer. Anal..

[3]  Graham F. Carey,et al.  Approximate boundary-flux calculations☆ , 1985 .

[4]  C. Dawson,et al.  Time-splitting methods for advection-diffusion-reaction equations arising in contaminant transport , 1992 .

[5]  Roy D. Williams,et al.  Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations , 2000 .

[6]  François Dubeau,et al.  Discontinuous polynomial approximations in the theory of one-step, hybrid and multistep methods for nonlinear ordinary differential equations , 1986 .

[7]  Graham F. Carey,et al.  Derivative calculation from finite element solutions , 1982 .

[8]  Mary F. Wheeler,et al.  A Galerkin Procedure for Estimating the Flux for Two-Point Boundary Value Problems , 1974 .

[9]  Tim Wildey,et al.  A posteriori error estimation and adaptive mesh refinement for a multiscale operator decomposition approach to fluid – solid heat transfer , 2010 .

[10]  Ivan Yotov,et al.  Interface solvers and preconditioners of domain decomposition type for multiphase flow in multiblock porous media , 2001 .

[11]  Daoqi Yang,et al.  A Parallel Nonoverlapping Schwarz Domain Decomposition Method for Elliptic Interface Problems , 1997 .

[12]  William W. Hager,et al.  Discontinuous Galerkin methods for ordinary differential equations , 1981 .

[13]  Andrew M. Stuart,et al.  The dynamical behavior of the discontinuous Galerkin method and related difference schemes , 2001, Math. Comput..

[14]  John N. Shadid,et al.  An A Posteriori-A Priori Analysis of Multiscale Operator Splitting , 2008, SIAM J. Numer. Anal..

[15]  D. Estep.  A posteriori error bounds and global error control for approximation of ordinary differential equations , 1995 .

[16]  Rolf Rannacher,et al.  Duality-based adaptivity in the hp-finite element method , 2003, J. Num. Math..

[17]  M. Ainsworth,et al.  Some useful techniques for pointwise and local error estimates of the quantities of interest in the finite element approximation , 2000 .

[18]  Claes Johnson,et al.  Computational Differential Equations , 1996 .

[19]  Endre Süli,et al.  Adaptive error control for finite element approximations of the lift and drag coefficients in viscous flow , 1997 .

[20]  D. Estep,et al.  Global error control for the continuous Galerkin finite element method for ordinary differential equations , 1994 .

[21]  John R. Rice,et al.  Interface Relaxation Methods for Elliptic Differential Equations , 2000 .

[22]  Michael J. Holst,et al.  Generalized Green's Functions and the Effective Domain of Influence , 2005, SIAM J. Sci. Comput..

[23]  Endre Süli,et al.  Adaptive finite element methods for differential equations , 2003, Lectures in mathematics.

[24]  L. R. Scott,et al.  The Mathematical Theory of Finite Element Methods , 1994 .