On one approach to a posteriori error estimates for evolution problems solved by the method of lines

[1]  Philippe G. Ciarlet,et al.  The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[2]  Ivo Babuška,et al.  A posteriori error estimation for the semidiscrete finite element method of parabolic differential equations , 2001 .

[3]  Giuseppe Savare',et al.  A posteriori error estimates for variable time-step discretizations of nonlinear evolution equations † , 2000 .

[4]  Karel Segeth,et al.  A posteriori error estimation with the finite element method of lines for a nonlinear parabolic equation in one space dimension , 1999, Numerische Mathematik.

[5]  Rüdiger Verfürth,et al.  A posteriori error estimates for nonlinear problems. Lr(0, T; Lrho(Omega))-error estimates for finite element discretizations of parabolic equations , 1998, Math. Comput..

[6]  Kenneth Eriksson,et al.  Adaptive finite element methods for parabolic problems IV: nonlinear problems , 1995 .

[7]  Ivo Babuška,et al.  Validation of A-Posteriori Error Estimators by Numerical Approach , 1994 .

[8]  I. Babuska,et al.  A model study of the quality of a posteriori error estimators for linear elliptic problems. Error estimation in the interior of patchwise uniform grids of triangles , 1994 .

[9]  Peter K. Moore,et al.  A posteriori error estimation with finite element semi- and fully discrete methods for nonlinear parabolic equations in one space dimension , 1994 .

[10]  Joseph E. Flaherty,et al.  A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems , 1993 .

[11]  Ivo Babuška,et al.  Analysis of the efficiency of an a posteriori error estimator for linear triangular finite elements , 1992 .

[12]  Kenneth Eriksson,et al.  Adaptive finite element methods for parabolic problems. I.: a linear model problem , 1991 .

[13]  J. Verwer,et al.  A numerical study of three moving-grid methods for one-dimensional partial differential equations which are based on the method of lines , 1990 .

[14]  J. T. Oden,et al.  A posteriori error estimation of finite element approximations in fluid mechanics , 1990 .

[15]  J. Oden,et al.  Toward a universal h - p adaptive finite element strategy: Part 2 , 1989 .

[16]  O. C. Zienkiewicz,et al.  Adaptive techniques in the finite element method , 1988 .

[17]  Joseph E. Flaherty,et al.  A moving finite element method with error estimation and refinement for one-dimensional time dependent partial differential equations , 1986 .

[18]  Ivo Babuška,et al.  Basic principles of feedback and adaptive approaches in the finite element method , 1986 .

[19]  Ivo Babuška,et al.  An adaptive method of lines with error control for parabolic equations of the reaction-diffusion type , 1986 .

[20]  R. Bank,et al.  Some a posteriori error estimators for elliptic partial differential equations , 1985 .

[21]  L. Petzold.  A description of dassl: a differential/algebraic system solver , 1982 .

[22]  A. Hindmarsh.  LSODE and LSODI, two new initial value ordinary differential equation solvers , 1980, SGNM.

[23]  E. Boschi.  Recensioni: J. L. Lions - Quelques méthodes de résolution des problémes aux limites non linéaires. Dunod, Gauthier-Vi;;ars, Paris, 1969; , 1971 .

[24]  C. Carstensen,et al.  Constants in Clément-interpolation error and residual based a posteriori estimates in finite element methods , 2000 .

[25]  M. Stynes,et al.  Numerical methods for singularly perturbed differential equations : convection-diffusion and flow problems , 1996 .

[26]  Rolf Rannacher,et al.  A Feed-Back Approach to Error Control in Finite Element Methods: Basic Analysis and Examples , 1996 .

[27]  Rüdiger Verführt,et al.  A review of a posteriori error estimation and adaptive mesh-refinement techniques , 1996, Advances in numerical mathematics.

[28]  K. Segeth.  A posteriori error estimates for parabolic differential systems solved by the finite element method of lines , 1994 .

[29]  K. Segeth.  Grid adjustment based on a posteriori error estimators , 1993 .

[30]  Karel Rektorys,et al.  The method of discretization in time and partial differential equations , 1982 .

[31]  I. Babuska,et al.  A‐posteriori error estimates for the finite element method , 1978 .

[32]  H. Baumgärtel,et al.  Gajewski, H./Gröger, K./Zacharias, K., Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, VI, 281 S. Berlin. Akademie-Verlag. 1974. Preis 65,- M . , 1977 .

[33]  P. Clément.  Approximation by finite element functions using local regularization , 1975 .

[34]  H. Gajewski,et al.  Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen , 1974 .