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A numerical method for backward parabolic problems with non-selfadjoint elliptic operators. (English) Zbl 0976.65080
A method for the solution of backward parabolic problems with non-selfadjoint elliptic operators is presented. The method employs a quasi-solution approach and is based on the separation of the problem into a sequence of well-posed forward problems on the entire mesh and an ill-posed system of algebraic equations on a coarser submesh. A stability result for the forward problem is obtained. Using this result, the existence of a quasi-solution of the backward problem is proved.

65M06Finite difference methods (IVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)
35K15Second order parabolic equations, initial value problems
Full Text: DOI
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