Kai Wang

Southern University of Science and Technology | SUSTech · Department of Mathematics

This article concerns numerical approximation of a parabolic interface problem with general L 2 initial value. The problem is discretized by a finite element method with a quasi-uniform triangulation of the domain fitting the interface, with piecewise linear approximation to the interface. The semi-discrete finite element problem is furthermore dis...

In a general polygonal domain, possibly nonconvex and multi-connected (with holes), the time-dependent Ginzburg-Landau equation is reformulated into a new system of equations. The magnetic field B := ∇×A is introduced as an unknown solution in the new system, while the magnetic potential A is solved implicitly through its Hodge decomposition into d...

We propose a fully discrete linearized Crank–Nicolson Galerkin–Galerkin finite element method for solving the partial differential equations which govern incompressible miscible flow in porous media. We prove optimal-order convergence of the fully discrete finite element solutions without any restrictions on the step size of time discretization. Nu...

The aim of this paper is to develop and analyze high-order time stepping schemes for solving semilinear subdiffusion equations. We apply the $k$-step BDF convolution quadrature to discretize the time-fractional derivative with order $\alpha\in (0,1)$, and modify the starting steps in order to achieve optimal convergence rate. This method has alread...

Purpose – The purpose of this paper is to find solution of Stokes flow problems with Dirichlet and Neumann boundary conditions in axisymmetry using an efficient non-singular method of fundamental solutions that does not require an artificial boundary, i.e. source points of the fundamental solution coincide with the collocation points on the boundar...

The solution of Stokes flow problems with Dirichlet and Neumann boundary conditions is performed by a non-singular method of fundamental solutions (MFS) which does not require artificial boundary, i.e., source points of fundamental solution coincide with the collocation points on the boundary. The fundamental solution of the Stokes pressure and vel...