L ∞ ( L 2 ) and L ∞ ( L ∞ ) error estimates for mixed methods for integro-differential equations of parabolic type

Ziwen Jiang

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1999)

  • Volume: 33, Issue: 3, page 531-546
  • ISSN: 0764-583X

How to cite

top

Jiang, Ziwen. "$L^\infty (L^2)$ and $L^\infty (L^\infty )$ error estimates for mixed methods for integro-differential equations of parabolic type." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 33.3 (1999): 531-546. <http://eudml.org/doc/193934>.

@article{Jiang1999,
author = {Jiang, Ziwen},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {mixed finite element method; initial-boundary value problems; parabolic integro-differential equation; error estimates},
language = {eng},
number = {3},
pages = {531-546},
publisher = {Dunod},
title = {$L^\infty (L^2)$ and $L^\infty (L^\infty )$ error estimates for mixed methods for integro-differential equations of parabolic type},
url = {http://eudml.org/doc/193934},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Jiang, Ziwen
TI - $L^\infty (L^2)$ and $L^\infty (L^\infty )$ error estimates for mixed methods for integro-differential equations of parabolic type
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1999
PB - Dunod
VL - 33
IS - 3
SP - 531
EP - 546
LA - eng
KW - mixed finite element method; initial-boundary value problems; parabolic integro-differential equation; error estimates
UR - http://eudml.org/doc/193934
ER -

References

top
  1. [1] J. R. Cannon and Y. Lin, A priori L2 error estimates for finite-element methods for nonlinear diffusion equations with memory. SIAM J. Numer. Anal. 27 (1990) 595-607. Zbl0709.65122MR1041253
  2. [2] J. R. Cannon and Y. Lin, Non-classical H1 projection and Galerkin methods for nonlinear parabohc Integro-differential equations. Calcolo 25 (1988) 187-201. Zbl0685.65124MR1053754
  3. [3] L. C. Cowsar, T. F. Dupont and M. F. Wheeler, A priori estimates for mixed finite element methods for the wave equations. Comput. Methods Appl. Mech. Engrg. 82 (1990) 205-222. Zbl0724.65087MR1077657
  4. [4] L. C. Cowsar, T. F. Dupont and M. F. Wheeler, A priori estimates for mixed finite element approximations of second-order hyperbolic equations with absorbing boundary conditions. SIAM J. Numer. Anal. 33 (1996) 492-504. Zbl0859.65097MR1388485
  5. [5] J. Jr. Douglas and J. E. Roberts, Global estimates for mixed methods for second order elliptic equations. Math. Comp. 44 (1985) 39-52. Zbl0624.65109MR771029
  6. [6] E. Greenwell-Yanik and G. Fairweather, Finite element methods for parabolic and hyperbolic partial integro-differential equations. Nonlinear Anal. 12 (1988) 785-809. Zbl0657.65142MR954953
  7. [7] M. N. Le Roux and V. Thomée, Numerical solution of semilinear integro-differential equations of parabolic type with nonsmooth data. SIAM J. Numer. Anal. 26 (1989) 1291-1309. Zbl0701.65091MR1025089
  8. [8] Y. Lin, Galerkin methods for nonlinear parabolic integro-differential equations with nonlinear boundary conditions. SIAM J. Numer. Anal. 27 (1990) 608-621. Zbl0703.65095MR1041254
  9. [9] F. A. Milner, Mixed finite element methods for Quasilinear second-order elliptic problems. Math. Comp. 44 (1985) 303-320. Zbl0567.65079MR777266
  10. [10] F. A. Milner and E.-J. Park, A mixed finite element method for a strongly nonlinear second-order elliptic problem. Math. Comp. 64 (1995) 973-988. Zbl0829.65128MR1303087
  11. [11] E. J. Park, Mixed finite element method for nonlinear second-order elliptic problems. SIAM J. Numer. Anal. 32 (1995) 865-885. Zbl0834.65108MR1335659
  12. [12] P. A. Raviart and J. M. Thomas, A mixed finite element method for 2-nd order elliptic problems, in Mathematical Aspects of the Finite Element Method. Lect. Notes Math. 606 (1977) 292-315. Zbl0362.65089MR483555
  13. [13] R. Scholtz, Optimal L∞-estimates for a mixed finite element method for second order elliptic and parabolic problems. Calcolo 20 (1983) 355-377. Zbl0571.65092MR761790
  14. [14] J. Squeff, Superconvergence of mixed finite element methods for parabohc equations. RAIRO Modél. Math. Anal. Numér. 21 (1987) 327-352. Zbl0621.65116MR896246
  15. [15] V. Thomée and N. Y. Zhang, Error estimates for semi-discrete finite element methods for parabohc integro-differential equations. Math. Comp. 53 (1989) 121-139. Zbl0673.65099MR969493
  16. [16] J. Wang, Asymptotic expansions and L∞-error estimates for mixed finite element methods for second order elliptic problems. Numer. Math. 55 (1989) 401-430. Zbl0676.65109MR997230

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.