Danping Yang

Inhomogeneous Dirichlet Boundary-Value Problems of Space-Fractional Diffusion Equations and their Finite Element Approximations

We prove the wellposedness of the Galerkin weak formulation and Petrov--Galerkin weak formulation for inhomogeneous Dirichlet boundary-value problems of constant- or variable-coefficient conservative Caputo space-fractional diffusion equations. We also show that the weak solutions to their Riemann--Liouville analogues do not exist, in general. In addition, we develop an indirect finite element method for the Dirichlet boundary-value problems of Caputo fractional differential equations, which reduces the computational work for the numerical solution of variable-coefficient fractional diffusion equations from

Finite Element Approximations of an Optimal Control Problem with Integral State Constraint

O(N^3)

Spectral mixed Galerkin method for state constrained optimal control problem governed by the first bi-harmonic equation

to

Domain Decomposition Methods for Nonlocal Total Variation Image Restoration

O(N)

An improved a posteriori error estimate for the Galerkin spectral method in one dimension

and the memory requirement from

Adaptive Finite Element Approximation for a Constrained Optimal Control Problem via Multi-meshes

O(N^2)

Parallel domain decomposition procedures of improved D-D type for parabolic problems

to

Sharp A Posteriori Error Estimates for Optimal Control Governed by Parabolic Integro-Differential Equations

O(N)

Ciarlet-Raviart mixed finite element approximation for an optimal control problem governed by the first bi-harmonic equation

on any quasiuniform space partition. We further prove a nearly sharp error estimate for the method, which is expressed in terms of the smoothness of the prescribed data of the problem only. We carry out numerical experiments to investigate the performance of the method in comparison with the Galerkin finite element method.

Parallel characteristic finite element method for time‐dependent convection–diffusion problem

An integral state-constrained optimal control problem governed by an elliptic partial differential equation and its finite element approximation are considered. The finite element approximation is constructed on multimeshes. An