The effect of inner products for discrete vector fields on the accuracy of mimetic finite difference methods

Computers and Mathematics with Applications

Volumn 42, Issue 12, 2001, Pages 1527-1547

  Hyman, J ^a   Shashkov, M ^a   Steinberg, S ^b  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b UNIVERSITY OF NEW MEXICO   (United States)

Author keywords

Accuracy; Discrete vector analysis; Finite difference methods; Inner products; Mimetic finite difference methods; Numerical analysis

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; FINITE ELEMENT METHOD; INTERPOLATION; MATHEMATICAL TRANSFORMATIONS; PARTIAL DIFFERENTIAL EQUATIONS; VECTORS;

ACCURACY; COMPUTER ALGEBRA; DISCRETE VECTOR FIELDS; ERROR ESTIMATION; INNER PRODUCTS; MIMETIC FINITE DIFFERENCE METHOD; PIOLA TRANSFORM; SUPPORT OPERATORS METHOD;

FINITE DIFFERENCE METHOD;

EID: 0035577026     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(01)00260-7     Document Type: Article

References (17)

1. Operational finite-difference schemes
2. Support-operator finite-difference algorithms for general elliptic problems
3. Solving diffusion equations with rough coefficients in rough grids
4. The construction of compatible hydrodynamics algorithms utilizing conservation of total energy
5. Natural discretizations for the divergence, gradient, and curl on logically rectangular grids
6. The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials
7. The adjoint operators for natural discretizations for the divergence, gradient and curl on logically rectangular grids
8. The approximation of boundary conditions for mimetic finite difference methods
9. Mimetic discretizations for Maxwell's equations
10. Using a curvilinear grid to construct symmetry-preserving discretization for Lagrangian gas dynamics
11. A discrete operator calculus for finite difference approximations
12. A local support-operator diffusion discretization scheme for quadrilateral r-z meshes
13. Enhanced cell-centered finite differences for elliptic equations on general geometry
14. Control-volume mixed finite element methods
15. The Fundamentals of Grid Generation
16. Analysis of material interface discontinuities and superconvergent fluxes in finite difference theory