On the asymptotic solution of an elliptic interior layer problem

N. G. Barton
1976 The Journal of the Australian Mathematical Society Series B Applied Mathematics  
An interior layer problem posed by an elliptic partial differential equation of the type e V 2 <£ -x3/dy = f(x, y, e ), 0 < e < 1, is investigated. This equation arises, for example, in the theory of rotating fluids and the important feature of the problem is an interior layer of width O(e'") in which the solution has a relatively large magnitude. The paper considers the simplest case which involves an interior layer, that is, where the domain is rectangular and f(x, y, e) = EA for A constant.
more » ... EA for A constant. A leading approximation is derived and it is shown to be asymptotic to the exact solution in nearly all of the domain as e ->0. The error estimates are derived using an a priori estimate for the solution of elliptic equations and a technique which optimizes the estimates is introduced. The applicability and limitations of the estimation technique are discussed briefly. 493 terms of use, available at https://www.cambridge.org/core/terms. https://doi.
doi:10.1017/s0334270000001351 fatcat:w6g5anxu6naptkevgxdxkf3xwi