Maximal regularity of multistep fully discrete finite element methods for parabolic equations

05/04/2020

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by   Buyang Li, et al.

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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+β, where d is the dimension of space and β>0. The maximal angles of R-boundedness are characterized for the analytic semigroup e^zA_h and the resolvent operator z(z-A_h)^-1, respectively, associated to an elliptic finite element operator A_h. Maximal L^p-regularity, optimal ℓ^p(L^q) error estimate, and ℓ^p(W^1,q) estimate are established for fully discrete finite element methods with multistep backward differentiation formula.