What is the bottom cross-section of the third order of accuracy?

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Multiple Choice

What is the bottom cross-section of the third order of accuracy?

The key idea is how grid resolution interacts with the order of accuracy. Third-order accuracy means the leading truncation error scales with the cube of the mesh size, so you need a grid fine enough to capture the solution’s variations with that cubic error behavior, but not so fine that you waste resources or violate domain constraints. The bottom cross-section refers to how many grid points lie along each horizontal direction at the base of the mesh. A 35 by 35 grid provides the needed balance: it’s fine enough to realize the third-order discretization error terms in the given domain and setup, yet not so fine as to be unnecessary or incompatible with the problem’s constraints. A coarser grid (like 25 by 25 or 20 by 20) would be too coarse to exhibit the third-order accuracy, while a much finer grid (like 40 by 40) exceeds what’s required under the problem’s conditions. Therefore, 35 by 35 is the correct cross-section.

The key idea is how grid resolution interacts with the order of accuracy. Third-order accuracy means the leading truncation error scales with the cube of the mesh size, so you need a grid fine enough to capture the solution’s variations with that cubic error behavior, but not so fine that you waste resources or violate domain constraints.

The bottom cross-section refers to how many grid points lie along each horizontal direction at the base of the mesh. A 35 by 35 grid provides the needed balance: it’s fine enough to realize the third-order discretization error terms in the given domain and setup, yet not so fine as to be unnecessary or incompatible with the problem’s constraints. A coarser grid (like 25 by 25 or 20 by 20) would be too coarse to exhibit the third-order accuracy, while a much finer grid (like 40 by 40) exceeds what’s required under the problem’s conditions. Therefore, 35 by 35 is the correct cross-section.

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