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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Nonelliptic approximation of a class of partial differential equations with Neumann boundary condition


Author: V. Girault
Journal: Math. Comp. 30 (1976), 68-91
MSC: Primary 65N30
MathSciNet review: 0395266
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Abstract: This paper is devoted to the numerical resolution of a class of linear partial differential equations with an inhomogeneous Neumann boundary condition. A first order quadrilateral finite element method is used, together with a one-point integration formula. The resulting scheme is simple and widely used but its theory is not classical, in a sense described as "nonelliptic". An important boundary value theorem is derived, in order to handle the Neumann condition. An error bound shows that the scheme is of order one.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1976-0395266-5
PII: S 0025-5718(1976)0395266-5
Keywords: Finite elements, discrete Green's formula, boundary values
Article copyright: © Copyright 1976 American Mathematical Society