Back to Search
Start Over
OPTIMAL-ORDER FINITE DIFFERENCE APPROXIMATION OF GENERALIZED SOLUTIONS TO THE BIHARMONIC EQUATION IN A CUBE.
- Source :
-
SIAM Journal on Numerical Analysis . 2020, Vol. 58 Issue 1, p298-329. 32p. - Publication Year :
- 2020
-
Abstract
- We prove an optimal-order error bound in the discrete H2() norm for finite difference approximations of the first boundary-value problem for the biharmonic equation in n space dimensions, with n 2 f2; : : : ; 7g, whose generalized solution belongs to the Sobolev space Hs()\H2 0 () for 1 2 max(5; n) < s 4, where = (0; 1)n. The result extends the range of the Sobolev index s in the best convergence results currently available in the literature to the maximal range admitted by the Sobolev embedding of Hs() into C() in n space dimensions. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FINITE differences
*BIHARMONIC equations
*SOBOLEV spaces
*CUBES
Subjects
Details
- Language :
- English
- ISSN :
- 00361429
- Volume :
- 58
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Numerical Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 144779595
- Full Text :
- https://doi.org/10.1137/19M1254313