Numerical analysis of nonlinear elliptic-parabolic equations

Emmanuel Maitre

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 36, Issue: 1, page 143-153
  • ISSN: 0764-583X

Abstract

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This paper deals with the numerical approximation of mild solutions of elliptic-parabolic equations, relying on the existence results of Bénilan and Wittbold (1996). We introduce a new and simple algorithm based on Halpern's iteration for nonexpansive operators (Bauschke, 1996; Halpern, 1967; Lions, 1977), which is shown to be convergent in the degenerate case, and compare it with existing schemes (Jäger and Kačur, 1995; Kačur, 1999).

How to cite

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Maitre, Emmanuel. "Numerical analysis of nonlinear elliptic-parabolic equations." ESAIM: Mathematical Modelling and Numerical Analysis 36.1 (2010): 143-153. <http://eudml.org/doc/194093>.

@article{Maitre2010,
abstract = { This paper deals with the numerical approximation of mild solutions of elliptic-parabolic equations, relying on the existence results of Bénilan and Wittbold (1996). We introduce a new and simple algorithm based on Halpern's iteration for nonexpansive operators (Bauschke, 1996; Halpern, 1967; Lions, 1977), which is shown to be convergent in the degenerate case, and compare it with existing schemes (Jäger and Kačur, 1995; Kačur, 1999). },
author = {Maitre, Emmanuel},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Elliptic-parabolic; numerical; iterative method.; elliptic-parabolic equation; mild solution; iterative method; convergence; numerical results},
language = {eng},
month = {3},
number = {1},
pages = {143-153},
publisher = {EDP Sciences},
title = {Numerical analysis of nonlinear elliptic-parabolic equations},
url = {http://eudml.org/doc/194093},
volume = {36},
year = {2010},
}

TY - JOUR
AU - Maitre, Emmanuel
TI - Numerical analysis of nonlinear elliptic-parabolic equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 36
IS - 1
SP - 143
EP - 153
AB - This paper deals with the numerical approximation of mild solutions of elliptic-parabolic equations, relying on the existence results of Bénilan and Wittbold (1996). We introduce a new and simple algorithm based on Halpern's iteration for nonexpansive operators (Bauschke, 1996; Halpern, 1967; Lions, 1977), which is shown to be convergent in the degenerate case, and compare it with existing schemes (Jäger and Kačur, 1995; Kačur, 1999).
LA - eng
KW - Elliptic-parabolic; numerical; iterative method.; elliptic-parabolic equation; mild solution; iterative method; convergence; numerical results
UR - http://eudml.org/doc/194093
ER -

References

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