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

Girault, V.

doi:10.1090/S0025-5718-1976-0395266-5

Nonelliptic approximation of a class of partial differential equations with Neumann boundary condition
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Math. Comp. 30 (1976), 68-91 Request permission

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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