Name
Abstract | ||
|---|---|---|
A new finite element method is proposed and analysed for second order elliptic equations using discontinuous piecewise polynomials on a finite element partition consisting of general polygons. The new method is based on a stabilization of the well-known primal hybrid formulation by using some least-squares forms imposed on the boundary of each element. Two finite element schemes are presented. The first one is a non-symmetric formulation and is absolutely stable in the sense that no parameter selection is necessary for the scheme to converge. The second one is a symmetric formulation, but is conditionally stable in that a parameter has to be selected in order to have an optimal order of convergence. Optimal-order error estimates in some H-1-equivalence norms are established for the proposed discontinuous finite element methods. For the symmetric formulation, an optimal-order error estimate is also derived in the L-2 norm. The new method features a finite element partition consisting of general polygons as opposed to triangles or quadrilaterals in the standard finite element Galerkin method. Copyright (C) 2002 John Wiley Sons, Ltd. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1002/nla.313 | NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS |
Keywords | Field | DocType |
finite element method,discontinuous Galerkin,elliptic problems,error estimates,mixed finite element method | Discontinuous Galerkin method,Boundary knot method,Mathematical optimization,Mathematical analysis,Superconvergence,Extended finite element method,Mathematics,hp-FEM,Smoothed finite element method,Mixed finite element method,Spectral element method | Journal |
Volume | Issue | ISSN |
10 | 1-2 | 1070-5325 |
Citations | PageRank | References |
8 | 1.49 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Richard E. Ewing | 1 | 252 | 45.87 |
| Junping Wang | 2 | 8 | 1.49 |
| Yongjun Yang | 3 | 8 | 1.49 |