We introduce an over-penalized weak Galerkin method for elliptic interface problems with non-homogeneous boundary conditions and discontinuous coefficients, where the combines a stabilizer interior penalty terms. This employs double-valued functions on edges of elements instead single-valued ones \begin{document}$ (\mathbb{P}_{k}, \...

This paper analyzes the local properties of the symmetric interior penalty upwind discontinuous Galerkin method (SIPG) for the numerical solution of optimal control problems governed by linear reaction-advection-diffusion equations with distributed controls. The theoretical and numerical results presented in this paper show that for advection-dominated problems the convergence properties of the...

By introducing the dimension splitting method (DSM) into improved interpolating moving least-squares (IMLS) with nonsingular weight function, a splitting–interpolating least squares (DS-IMLS) is first proposed. Since DSM can decompose problem series of lower-dimensional problems, DS-IMLS reduce matrix in calculating shape function and computational complexity derivatives approximation function....

In this paper we describe the discontinuous Galerkin time-domain method and apply it to the simulation of ground-penetrating radar (GPR) problems in 3D. The method is first validated with analytical solutions and we show its superior behaviour when compared to the classical finite-difference time-domain method, widely employed in GPR simulation. In the discontinuous Galerkin time-domain the sol...

A systematic numerical study on weak Galerkin (WG) finite element method for second order linear parabolic problems is presented by allowing polynomial approximations with various degrees each local element. Convergence of both semidiscrete and fully discrete WG solutions are established in $L^{\infty}(L^2)$ $L^{\infty}(H^1)$ norms a general $({\cal P}_{k}(K),\;{\cal P}_{j}(\partial K),\;\big[{...