Combining maximal regularity and energy estimates for time discretizations of quasilinear parabolic equations

• DOI: 10.1090/mcom/3228
• Publication Date: 2016-10-26T14:02:02Z
• Authors: Georgios Akrivis; Buyang Li; Christian Lubich
• Keywords: FOS: Mathematics; Mathematics - Numerical Analysis; Numerical Analysis (math.NA); 0101 mathematics; 01 natural sciences; 510

We analyze fully implicit and linearly backward difference formula (BDF) methods for quasilinear parabolic equations, without making any assumptions on the growth or decay of coefficient functions. combine maximal regularity energy estimates to derive optimal-order error bounds time-discrete approximation solution its gradient in maximum norm norm.