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Mesh‐centered finite differences from nodal finite elements for elliptic problems
Author(s) -
Hennart J. P.,
del Valle E.
Publication year - 1998
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199807)14:4<439::aid-num2>3.0.co;2-l
Subject(s) - mathematics , quadrature (astronomy) , finite element method , polygon mesh , finite difference , boundary value problem , finite difference method , finite difference coefficient , mathematical analysis , cardinal point , mixed finite element method , geometry , physics , optics , electrical engineering , thermodynamics , engineering
After it is shown that the classical five‐point mesh‐centered finite difference scheme can be derived from a low‐order nodal finite element scheme by using nonstandard quadrature formulae, higher‐order block mesh‐centered finite difference schemes for second‐order elliptic problems are derived from higher‐order nodal finite elements with nonstandard quadrature formulae as before, combined to a procedure known as “transverse integration.” Numerical experiments with uniform and nonuniform meshes and different types of boundary conditions confirm the theoretical predictions, in discrete as well as continuous norms. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 439–465, 1998