Name
Title | ||
|---|---|---|
On the Accuracy of the Finite Volume Element Method Based on Piecewise Linear Polynomials |
Abstract | ||
|---|---|---|
We present a general error estimation framework for a finite volume element (FVE) method based on linear polynomials for solving second-order elliptic boundary value problems. This framework treats the FVE method as a perturbation of the Galerkin finite element method and reveals that regularities in both the exact solution and the source term can affect the accuracy of FVE methods. In particular, the error estimates and counterexamples in this paper will confirm that the FVE method cannot have the standard O(h2) convergence rate in the L2 norm when the source term has the minimum regularity, only being in L2, even if the exact solution is in H2. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1137/S0036142900368873 | SIAM Journal on Numerical Analysis |
Keywords | Field | DocType |
linear polynomial,piecewise linear polynomials,error estimate,finite volume element,general error estimation framework,finite volume,source term,fve method,exact solution,elliptic,counterexamples,l2 norm,error estimates,convergence rate,galerkin finite element method,element method,elliptic boundary value problem,finite element method,piecewise linear,generalization error | Mathematical optimization,Polynomial,Mathematical analysis,Galerkin method,Finite element method,Rate of convergence,Numerical analysis,Partial differential equation,Piecewise linear function,Finite volume method,Mathematics | Journal |
Volume | Issue | ISSN |
39 | 6 | 0036-1429 |
Citations | PageRank | References |
65 | 5.12 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Richard E. Ewing | 1 | 252 | 45.87 |
| Tao Lin | 2 | 152 | 15.03 |
| Yanping Lin | 3 | 244 | 26.94 |