Maximal regularity of multistep fully discrete finite element methods for parabolic equations
Abstract
This article extends the semidiscrete maximal $L^p$regularity results in [27] to multistep fully discrete finite element methods for parabolic equations with more general diffusion coefficients in $W^{1,d+\beta}$, where $d$ is the dimension of space and $\beta>0$. The maximal angles of $R$boundedness are characterized for the analytic semigroup $e^{zA_h}$ and the resolvent operator $z(zA_h)^{1}$, respectively, associated to an elliptic finite element operator $A_h$. Maximal $L^p$regularity, optimal $\ell^p(L^q)$ error estimate, and $\ell^p(W^{1,q})$ estimate are established for fully discrete finite element methods with multistep backward differentiation formula.
 Publication:

arXiv eprints
 Pub Date:
 May 2020
 DOI:
 10.48550/arXiv.2005.01408
 arXiv:
 arXiv:2005.01408
 Bibcode:
 2020arXiv200501408L
 Keywords:

 Mathematics  Numerical Analysis