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Unified approach to numerical methods, part II: Finite elements, boundary methods, and their coupling
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.1690010302
Subject(s) - mathematics , finite element method , boundary value problem , partial differential equation , boundary (topology) , numerical analysis , coupling (piping) , boundary knot method , mathematical analysis , boundary element method , mechanical engineering , physics , engineering , thermodynamics
This is the second in a series of three papers devoted to the presentation of a direct procedure of analysis of numerical methods for partial differential equations. The procedure consists of applying the method of weighted residuals and then interpreting the resulting equations by means of Green's formulas for discontinuous functions. Here, the general Green's formulas for operators defined in discontinuous fields developed in the first article, are applied to formulate the method of weighted residuals for arbitrary linear operators. Finite elements, boundary methods, and general procedures for coupling finite elements and boundary methods are discussed.