Abstract
We analyze fully implicit and linearly implicit backward difference formula (BDF) methods for quasilinear parabolic equations, without making any assumptions on the growth or decay of the coefficient functions. We combine maximal parabolic regularity and energy estimates to derive optimal-order error bounds for the time-discrete approximation to the solution and its gradient in the maximum norm and energy norm.
| Original language | English |
|---|---|
| Pages (from-to) | 1527-1552 |
| Number of pages | 26 |
| Journal | Mathematics of Computation |
| Volume | 86 |
| Issue number | 306 |
| DOIs | |
| Publication status | Published - 1 Jan 2017 |
Keywords
- BDF methods
- Energy technique
- Maximal regularity
- Maximum norm estimates
- Parabolic equations
- Stability
ASJC Scopus subject areas
- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics
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