Xiu Ye

A computational study of the weak Galerkin method for second-order elliptic equations

The weak Galerkin finite element method is a novel numerical method that was first proposed and analyzed by Wang and Ye (2011) for general second order elliptic problems on triangular meshes. The goal of this paper is to conduct a computational investigation for the weak Galerkin method for various model problems with more general finite element partitions. The numerical results confirm the theory established in Wang and Ye (2011). The results also indicate that the weak Galerkin method is efficient, robust, and reliable in scientific computing.

Discontinuous Galerkin Finite Element Methods for Interface Problems: A Priori and A Posteriori Error Estimations

Discontinuous Galerkin (DG) finite element methods were studied by many researchers for second-order elliptic partial differential equations, and a priori error estimates were established when the solution of the underlying problem is piecewise

Unified Analysis of Finite Volume Methods for Second Order Elliptic Problems

H^{3/2+\epsilon}

A Discontinuous Finite Volume Method for the Stokes Problems

smooth with

A New Discontinuous Finite Volume Method for Elliptic Problems

\epsilon>0

A Weak Galerkin Finite Element Method for the Maxwell Equations

. However, elliptic interface problems with intersecting interfaces do not possess such a smoothness. In this paper, we establish a quasi-optimal a priori error estimate for interface problems whose solutions are only

A \(C^0\)-Weak Galerkin Finite Element Method for the Biharmonic Equation

H^{1+\alpha}

A stable numerical algorithm for the Brinkman equations by weak Galerkin finite element methods

smooth with

Unified Analysis of Finite Volume Methods for the Stokes Equations

\alpha\in(0,1)

A Robust Numerical Method for Stokes Equations Based on Divergence-Free

and, hence, fill a theoretical gap of the DG method for elliptic problems with low regularity. The second part of the paper deals with the design and analysis of robust residual- and recovery-based a posteriori error estimators. Theoretically, we show that the residual and recovery estimators studied in this paper are robust with respect to the DG norm, i.e., their reliability and efficiency bounds do not depend on the jump, provided that the distribution of coefficients is locally quasi-monotone.