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We analyze the three-stage symmetrized locally 1D finite-difference scheme for solving an initial-boundary value problem for the 2D heat equation. Error bounds of orders and related ones are proved for nonsmooth data. The sharpness in order  of these in a strong sense is confirmed by deriving the corresponding lower error bounds. The error bounds are, in the main, worse than the known optimal error bounds that are valid, for example, for the symmetric scheme. The above confirms the general conclusion that symmetrized locally 1D methods cannot serve as optimal methods for solving parabolic problems.

Sharp Error Bounds for a Symmetrized Locally 1d Method for Solving the 2d Heat Equation