253 citations · 476 across the 75 of their papers we have counts for
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Global well-posedness of the time-dependent Ginzburg-Landau superconductivity model in curved polyhedra
Buyang Li, Chaoxia Yang
We study the time-dependent Ginzburg--Landau equations in a three-dimensional curved polyhedron (possibly nonconvex). Compared with the previous works, we prove existence and uniqu…
A bounded numerical solution with a small mesh size implies existence of a smooth solution to the Navier-Stokes equations
Buyang Li
We prove that for a given smooth initial value, if the finite element solution of the three-dimensional Navier-Stokes equations is bounded in a certain norm with a relatively small…
A new approach for numerical simulation of the time-dependent Ginzburg-Landau equations
Buyang Li, Zhimin Zhang
We introduce a new approach for finite element simulations of the time-dependent Ginzburg-Landau equations (TDGL) in a general curved polygon, possibly with reentrant corners. Spec…
Mathematical and numerical analysis of time-dependent Ginzburg--Landau equations in nonconvex polygons based on Hodge decomposition
Buyang Li, Zhimin Zhang
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 th…
Convergence of a decoupled mixed FEM for miscible displacement in interfacial porous media
Buyang Li, Hongxing Rui, Chaoxia Yang
In this paper, we study the stability and convergence of a decoupled and linearized mixed finite element method (FEM) for incompressible miscible displacement in a porous media who…
Regularity of the diffusion-dispersion tensor and error analysis of Galerkin FEMs for a porous media flow
Buyang Li, Weiwei Sun
We study Galerkin finite element methods for an incompressible miscible flow in porous media with the commonly-used Bear-Scheidegger diffusion-dispersion tensor $D({\bf u}) = Φd_m…
A singular integral approach to the maximal L^p regularity of parabolic equations
Buyang Li
Here we describe a simple and fundamental approach to the maximal L^p regularity of parabolic equations, which only uses the concept of singular integrals of Volterra type. Knowled…