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Unified formulation of numerical methods. I. Green's formulas for operators in discontinuous fields
Author(s) -
Herrera Ismael
Publication year - 1985
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/num.1690010105
Subject(s) - mathematics , scheme (mathematics) , sequence (biology) , finite element method , boundary value problem , green s , mathematical analysis , calculus (dental) , algebra over a field , pure mathematics , genetics , physics , medicine , dentistry , biology , thermodynamics
Applying the method of weighted residuals and then interpreting the resulting equations by means of Green's formulas for discontinuous functions, a direct method of analysis is developed. The scheme includes finite differences, finite elements, and boundary methods. This is the first of a sequence of articles in which the methodology is presented. A fundamental ingredient of the procedure are general Green's formulas for operators defined in discontinuous fields. They are developed in this first article.