2 citations · 3 across the 5 of their papers we have counts for
5 papers
Super-approximation and optimal convergence of the stabilized BGN method with piecewise linear parametric finite elements for curve-shortening flow
Genming Bai
We develop a bihomotopy argument to estimate the discrete material time derivatives of consistency functionals. Combined with summation-by-parts, this argument yields a directional…
Stabilization and optimal convergence of Dziuk's method with piecewise linear parametric finite elements for curve-shortening flow
Genming Bai
We propose a stabilized version of the fully discrete Dziuk's method for the curve-shortening flow of a closed planar curve with piecewise linear parametric finite elements. With a…
Maximal regularity of evolving FEMs for parabolic equations on an evolving surface
Genming Bai, Balázs Kovács, Buyang Li
In this paper, we prove that spatially semi-discrete evolving finite element method for parabolic equations on a given evolving hypersurface of arbitrary dimensions preserves the m…
Weak maximum principle of finite element methods for parabolic equations in polygonal domains
Genming Bai, Dmitriy Leykekhman, Buyang Li
The weak maximum principle of finite element methods for parabolic equations is proved for both semi-discretization in space and fully discrete methods with -step backward diffe…
Physics Informed Neural Networks (PINNs)for approximating nonlinear dispersive PDEs
Genming Bai, Ujjwal Koley, Siddhartha Mishra +1
We propose a novel algorithm, based on physics-informed neural networks (PINNs) to efficiently approximate solutions of nonlinear dispersive PDEs such as the KdV-Kawahara, Camassa-…