Some errors estimates for the box method
@article{Bank1987SomeEE, title={Some errors estimates for the box method}, author={Randolph E. Bank and Donald J. Rose}, journal={SIAM Journal on Numerical Analysis}, year={1987}, volume={24}, pages={777-787} }
We define and analyze several variants of the box method for discretizing elliptic boundary value problems in the plane. Our estimates show the error to be comparable to a standard Galerkin finite element method using piecewise linear polynomials.
436 Citations
Finite volume element methods for non-definite problems
- BusinessNumerische Mathematik
- 1999
A simple upwind scheme is proven to be unconditionally stable and first order accurate in finite volume element method applied to 2 and 3-D non-definite problems.
A POSTERIORI ERROR ESTIMATOR FOR NONCONFORMING FINITE VOLUME ELEMENT APPROXIMATIONS OF THE STOKES PROBLEM
- Computer Science
- 2011
In this article, a posteriori error analysis of a finite volume element method based on the nonconforming element for the two-dimensional Stokes equations is investigated. An explicit residual-based…
A diffuse interface box method for elliptic problems
- Computer Science, MathematicsAppl. Math. Lett.
- 2021
Discontinuous finite volume element method for parabolic problems
- Mathematics
- 2009
In this article, we consider the semidiscrete and the backward Euler fully discrete discontinuous finite volume element methods for the second‐order parabolic problems and obtain the optimal order…
A residual-type a posteriori error estimate of finite volume element method for a quasi-linear elliptic problem
- Mathematics, Computer ScienceNumerische Mathematik
- 2009
A residual-type a posteriori error estimator of the finite volume element method for a quasi-linear elliptic problem of nonmonotone type is analyzed and computable upper and lower bounds on the error in the H1-norm are derived.
Error Estimates for a Finite Volume Element Method for Elliptic PDEs in Nonconvex Polygonal Domains
- Mathematics, Computer ScienceSIAM J. Numer. Anal.
- 2005
Standard finite volume piecewise linear approximations for second order elliptic boundary value problems on a nonconvex polygonal domain are considered, based on sharp shift estimates, and error estimations in H1-, L2- and L-norms are derived, taking into consideration the regularity of the data.
Finite Volume Methods for Elliptic PDE's: A New Approach
- Mathematics
- 2002
We consider a new formulation for finite volume element methods, which is satisfied by known finite volume methods and it can be used to introduce new ones. This framework results by approximating…
A PIECEWISE LINEAR PETROV-GALERKIN ANALYSIS OF THE BOX-METHOD
- Mathematics
- 1994
For the type of boundary value problems which figure in the drift-diffusion semiconductor model, the perpendicular-bisecting box-method discretization yields M-matrices and maximum stability on…
A projection approach to finite volume discretization of diffusion operators
- Computer Science
- 2008
This work proposes a new approach to cell centered finite volume discretization of elliptic problems, using triangular meshes in R as an example, and defines derivatives of piecewise constant approximations using a finite element approach.
Interior Estimates of Finite Volume Element Methods Over Quadrilateral Meshes for Elliptic Equations
- MathematicsSIAM J. Numer. Anal.
- 2019
The interior error estimates of a class of finite volume element methods (FVEMs) over quadrilateral meshes for elliptic equations are studied.
References
SHOWING 1-10 OF 10 REFERENCES
Lectures on Elliptic Boundary Value Problems
- Mathematics
- 1965
This book, which is a new edition of a book originally published in 1965, presents an introduction to the theory of higher-order elliptic boundary value problems. The book contains a detailed study…
Numerical methods for semiconductor device simulation
- Computer ScienceIEEE Transactions on Electron Devices
- 1983
This paper describes the numerical techniques used to solve the coupled system of nonlinear partial differential equations which model semiconductor devices, and the efficient solution of the resulting nonlinear and linear algebraic equations.
SOME SUPERCONVERGENCE RESULTS FOR MIXED FINITE ELEMENT METHODS FOR ELLIPTIC PROBLEMS ON RECTANGULAR DOMAINS.
- Mathematics
- 1985
The numerical solution of second-order boundary value problems on nonuniform meshes
- Mathematics, Computer Science
- 1986
It is shown that certain commonly used difference schemes yield second-order accurate solutions despite the fact that their truncation error is of lower order, which illuminates a limitation of the standard stability, consistency proof of convergence for difference schemes defined on nonuniform meshes.
Matrix Iterative Analysis
- Mathematics
- 1961
Matrix Properties and Concepts.- Nonnegative Matrices.- Basic Iterative Methods and Comparison Theorems.- Successive Overrelaxation Iterative Methods.- Semi-Iterative Methods.- Derivation and…
Homogeneous diierence shemes on nonuniform nets
- Zh. Vychist. Mat. i. Fiz. V1
- 1962
Supraconvergent schemes on irregular grids, tech. rep., Los Alamos National Laboratory
- Supraconvergent schemes on irregular grids, tech. rep., Los Alamos National Laboratory
- 1983
Homogeneous di erence shemes on nonuniform nets
- Zh . Vychist . Mat . i . Fiz . V
Some superconvergence results for mixed nite element methods for elliptic problems on rectangular domains, tech. rep
- Some superconvergence results for mixed nite element methods for elliptic problems on rectangular domains, tech. rep
- 1984