| Title:
|
Smoothing effect and discretization in time to semilinear parabolic equations with nonsmooth data (English) |
| Author:
|
Slodička, Marian |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
4 |
| Year:
|
1991 |
| Pages:
|
703-713 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The purpose of this paper is to derive the error estimates for discretization in time of a semilinear parabolic equation in a Banach space. The estimates are given in the norm of the space $\Bbb X_{\alpha }$ for $0<\alpha <1$ when the initial condition is not regular. (English) |
| Keyword:
|
error estimates |
| Keyword:
|
parabolic equation |
| Keyword:
|
backward Euler method |
| Keyword:
|
nonsmooth initial data |
| MSC:
|
34G20 |
| MSC:
|
35G10 |
| MSC:
|
35K22 |
| MSC:
|
35K25 |
| MSC:
|
35R20 |
| MSC:
|
65J15 |
| MSC:
|
65M15 |
| MSC:
|
65M20 |
| idZBL:
|
Zbl 0755.65095 |
| idMR:
|
MR1159817 |
| . |
| Date available:
|
2009-01-08T17:48:26Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118450 |
| . |
| Reference:
|
[1] Helfrich H.-P.: Error estimates for semidiscrete Galerkin type approximations to semilinear evolution equations with nonsmooth initial data.Numer. Math. 51 (1987), 559-569. Zbl 0648.65078, MR 0910865 |
| Reference:
|
[2] Henry D.: Geometric Theory of Semilinear Parabolic Equations.Lecture Notes in Math. 840, Springer Verlag, Berlin-Heidelberg-New York, 1981. Zbl 0663.35001, MR 0610244 |
| Reference:
|
[3] Johnson C., Larsson S., Thomee V., Wahlbin L.B.: Error estimates for spatially discrete approximations of semilinear parabolic equations with nonsmooth initial data.Math. Comp. 49 (1987), 331-357. Zbl 0634.65110, MR 0906175 |
| Reference:
|
[4] Le Roux M.-N.: Semidiscretization in time for parabolic problems.Math. Comp. 33 (1979), 919-931. Zbl 0417.65049, MR 0528047 |
| Reference:
|
[5] Le Roux M.-N., Thomee V.: Numerical solution of semilinear integrodifferential equations of parabolic type with nonsmooth data.SIAM J. Numer. Anal. 26 (1989), 1291-1309. Zbl 0701.65091, MR 1025089 |
| Reference:
|
[6] Luskin M., Rannacher R.: On the smoothing property of the Galerkin method for parabolic equations.SIAM J. Numer. Anal. 19 (1982), 93-113. Zbl 0483.65064, MR 0646596 |
| Reference:
|
[7] Mingyou H., Thomee V.: On the backward Euler method for parabolic equations with rough initial data.SIAM J. Numer. Anal. 19 (1982), 599-603. Zbl 0482.65051, MR 0656473 |
| Reference:
|
[8] Sammon P.H.: Convergence estimates for semidiscrete parabolic equation approximations.SIAM J. Numer. Anal. 19 (1982), 68-92. Zbl 0497.65056, MR 0646595 |
| Reference:
|
[9] Slodička M.: Error estimates for discretization in time to linear homogeneous parabolic equations with nonsmooth initial data.preprint JINR, E5-90-08, Dubna, 1990. |
| Reference:
|
[10] Slodička M.: Error estimates for discretization in time to nonhomogeneous parabolic equations with rough initial data.preprint JINR, E5-90-212, Dubna, 1990. |
| Reference:
|
[11] Taylor A.E.: Introduction to Functional Analysis.Wiley, New York, 1958. Zbl 0654.46002, MR 0098966 |
| Reference:
|
[12] Thomee V.: Galerkin Finite Element Methods for Parabolic Problems.Lecture Notes in Math. 1054, Springer Verlag, Berlin-Heidelberg-New York-Tokyo, 1984. Zbl 1105.65102, MR 0744045 |
| Reference:
|
[13] Thomee V.: On the numerical solution of integro-differential equations of parabolic type.Inter. Ser. of Numer. Math., vol. 86, Birkhäuser Verlag Basel, 1988, pp. 477-493. Zbl 0658.65142, MR 1022978 |
| Reference:
|
[14] Thomee V., Zhang N.-Y.: Error estimates for semidiscrete finite element methods for parabolic integro-differential equations.Math. Comp. 53 (1989), 121-139. Zbl 0673.65099, MR 0969493 |
| . |
