Abstract

The well‐posedness of the Bitsadze‐Samarskii type nonlocal boundary value problem for abstract elliptic equations in Bochner spaces is established. The second order of accuracy difference scheme for the approximate solution of this problem is considered. The coercive inequalities for the solution of this difference scheme are established. In applications, the almost coercive stability and the coercive stability estimates for the solution of difference schemes for the approximate solution of the nonlocal boundary value problem for the elliptic equation are obtained.

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