6 papers
Numerical analysis of two Galerkin discretizations with graded temporal grids for fractional evolution equations
Binjie Li, Tao Wang, Xiaoping Xie
Two numerical methods with graded temporal grids are analyzed for fractional evolution equations. One is a low-order discontinuous Galerkin (DG) discretization in the case of fract…
Discontinuous Galerkin method for a distributed optimal control problem governed by a time fractional diffusion equation
Tao Wang, Binjie Li, Xiaoping Xie
This paper is devoted to the numerical analysis of a control constrained distributed optimal control problem subject to a time fractional diffusion equation with non-smooth initial…
Numerical analysis of a semilinear fractional diffusion equation
Binjie Li, Tao Wang, Xiaoping Xie
This paper considers the numerical analysis of a semilinear fractional diffusion equation with nonsmooth initial data. A new Grönwall's inequality and its discrete version are prop…
Analysis of a time-stepping discontinuous Galerkin method for fractional diffusion-wave equation with nonsmooth data
Binjie Li, Tao Wang, Xiaoping Xie
This paper analyzes a time-stepping discontinuous Galerkin method for fractional diffusion-wave problems. This method uses piecewise constant functions in the temporal discretizati…
Analysis of the L1 scheme for fractional wave equations with nonsmooth data
Binjie Li, Tao Wang, Xiaoping Xie
This paper analyzes the well-known L1 scheme for fractional wave equations with nonsmooth data. A new stability estimate is obtained, and the temporal accuracy $ \mathcal O(τ^{3-α}…
Separable functions: symmetry, monotonicity, and applications
Tao Wang, Taishan Yi
In this paper, we introduce concepts of separable functions in balls and in the whole space, and develop a new method to investigate the qualitative properties of separable functio…