In this paper, we investigate a residual-based posteriori error estimates for the hp finite element approximation of general optimal control problems governed by bilinear elliptic equations. By using the hp discontinuous Galerkin finite element approximation for the control and the hp finite element approximation for both the state and the co-state, we derive a posteriori upper error bounds for...

The generalized weak Galerkin (gWG) finite element method is proposed and analyzed for the biharmonic equation. A new discrete second order partial derivative introduced in gWG scheme to allow arbitrary combinations of piecewise polynomial functions defined interior on boundary general polygonal or polyhedral elements. error estimates are established numerical approximation a H2 norm L2 norm. r...

This article introduces a weak Galerkin (WG) finite element method for quad-curl problems in three dimensions. It is proved that the proposed WG stable and accurate an optimal order of error estimates exact solution discrete norms. In addition, L2 estimate except lowest k=2 derived solution. Some numerical experiments are conducted to verify efficiency accuracy our furthermore superconvergence ...

The present work is concerned with the analysis of the Discontinuous Galerkin Finite Element Method (DGFEM) for linear • diffusion problems, • elasticity problems,

Spatial Galerkin projection transfers fields between different meshes. In the area of finite element analysis of electromagnetic fields, it provides great convenience for remeshing, multi-physics, domain decomposition methods, etc. In this paper, a space-time Galerkin projection is developed in order to transfer fields between different spatial and temporal discretization bases.

In this paper, we consider the issue of convergence toward entropy solutions for high order finite volume weighted essentially non-oscillatory (WENO) scheme and discontinuous Galerkin (DG) finite element method approximating scalar nonconvex conservation laws. Although such high order nonlinearly stable schemes can usually converge to entropy solutions of convex conservation laws, convergence m...