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We consider the analysis and numerical solution of a forward-backward boundary value problem. We provide some motivation, prove existence and uniqueness in a function class especially geared to the problem at hand} provide various energy estimâtes, prove a priori error estimâtes for the Galerkin method, and show the results of some numerical computations. AMS Subject Classification. 65M60, 65N30, 65N15, 76D15, 76M10.

Origins, analysis, numerical analysis, and numerical approximation of a forward-backward parabolic problem