Buyang Li

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

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.

Mathematical and numerical analysis of the time-dependent Ginzburg-Landau equations in nonconvex polygons based on hodge decomposition

We prove well-posedness of time-dependent Ginzburg--Landau system in a nonconvex polygonal domain, and decompose the solution as a regular part plus a singular part. We see that the magnetic potential is not in

Discrete maximal regularity of time-stepping schemes for fractional evolution equations

H^1

Correction of High-Order BDF Convolution Quadrature for Fractional Evolution Equations

in general, and the finite element method (FEM) may give incorrect solutions. To remedy this situation, we reformulate the equations into an equivalent system of elliptic and parabolic equations based on the Hodge decomposition, which avoids direct calculation of the magnetic potential. The essential unknowns of the reformulated system admit

Convergence of finite elements on an evolving surface driven by diffusion on the surface

H^1

Numerical Analysis of Nonlinear Subdiffusion Equations

solutions and can be solved correctly by the FEMs. We then propose a decoupled and linearized FEM to solve the reformulated equations and present error estimates based on proved regularity of the solution. Numerical examples are provided to support our theoretical analysis and show the efficiency of the method.

Runge–Kutta Time Discretization of Nonlinear Parabolic Equations Studied via Discrete Maximal Parabolic Regularity

In this work, we establish the maximal

Analyticity, maximal regularity and maximum-norm stability of semi-discrete finite element solutions of parabolic equations in nonconvex polyhedra

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