Higher order derivative estimates for finite-difference schemes
arXiv:0805.31498 citationsh-index: 47
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This work offers theoretical guarantees for higher-order derivative estimates in numerical schemes, which is important for the reliability of finite-difference methods in scientific computing.
The paper provides sufficient conditions for finite-difference schemes solving second-order degenerate parabolic and elliptic equations to have mesh-independent estimates of spatial derivatives up to any order.
We give sufficient conditions under which solutions of finite-difference schemes in the space variable for second order possibly degenerate parabolic and elliptic equations admit estimates of spatial derivatives up to any given order independent of the mesh size.