A posteriori error estimator framework for PDE's

[1]  J. Oden,et al.  A Posteriori Error Estimation in Finite Element Analysis , 2000 .

[2]  I. Celik,et al.  Limitations of Richardson Extrapolation and Some Possible Remedies , 2005 .

[3]  Donald Estep,et al.  Analysis of shear layers in a fluid with temperature-dependent viscosity , 2001 .

[4]  Wei Shyy,et al.  COMPUTATIONS OF DROP DYNAMICS WITH THE IMMERSED BOUNDARY METHOD, PART 1: NUMERICAL ALGORITHM AND BUOYANCY-INDUCED EFFECT , 2003 .

[5]  J. Z. Zhu,et al.  The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity , 1992 .

[6]  P. Knupp,et al.  Completed Richardson extrapolation , 1993 .

[7]  Nicholas J. Higham,et al.  Experience with a Matrix Norm Estimator , 1990, SIAM J. Sci. Comput..

[8]  Wei Shyy,et al.  COMPUTATIONS OF DROP DYNAMICS WITH THE IMMERSED BOUNDARY METHOD, PART 2: DROP IMPACT AND HEAT TRANSFER , 2003 .

[9]  M. Garbey,et al.  A least square extrapolation method for improving solution accuracy of PDE computations , 2003 .

[10]  Åke Björck,et al.  Numerical methods for least square problems , 1996 .

[11]  James Glimm,et al.  Computational methods for statistical solutions of inverse problems for flow in porous media , 2000 .

[12]  Nicholas J. Higham,et al.  FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation , 1988, TOMS.

[13]  Slimane Adjerid,et al.  A posteriori discontinuous finite element error estimation for two-dimensional hyperbolic problems , 2002 .

[14]  J.-P. Pelle,et al.  A posteriori error estimation for unilateral contact with matching and non-matching meshes , 2000 .

[15]  Carsten Carstensen,et al.  Averaging technique for FE – a posteriori error control in elasticity. Part I: Conforming FEM , 2001 .

[16]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[17]  C. Peskin.  The immersed boundary method , 2002, Acta Numerica.

[18]  DAVID KAY,et al.  A Posteriori Error Estimation for Stabilized Mixed Approximations of the Stokes Equations , 1999, SIAM J. Sci. Comput..

[19]  Anthony T. Patera,et al.  A posteriori finite-element output bounds for the incompressible Navier-Stokes equations: application to a natural convection problem , 2001 .

[20]  Marc Garbey,et al.  A least square extrapolation method for the a posteriori error estimate of the incompressible Navier Stokes problem , 2005 .

[21]  David H. Sharp,et al.  Stochastic methods for the prediction of complex multiscale phenomena , 1998 .

[22]  J. Peraire,et al.  A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations , 1997 .

[23]  Jinchao Xu,et al.  Assessment of Numerical Accuracy of PDF/Monte Carlo Methods for Turbulent Reacting Flows , 1999 .

[24]  W. Eckhaus.  Asymptotic Analysis of Singular Perturbations , 1979 .

[25]  Ilaria Perugia,et al.  An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems , 2000, SIAM J. Numer. Anal..

[26]  Bernardo Cockburn,et al.  A posteriori error estimates for general numerical methods for Hamilton-Jacobi equations. Part I: The steady state case , 2001, Math. Comput..

[27]  J. Z. Zhu,et al.  The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique , 1992 .

[28]  Slimane Adjerid,et al.  A posteriori error estimates for fourth-order elliptic problems , 2002 .

[29]  Bernardo Cockburn,et al.  Optimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for convection-diffusion problems , 2002, Math. Comput..