First derivatives estimates for finite-difference schemes
arXiv:0802.11806 citationsh-index: 47
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It addresses a fundamental numerical analysis problem for researchers working on finite-difference methods for PDEs.
The paper provides sufficient conditions for finite-difference schemes to yield first derivative estimates independent of mesh size for second-order parabolic and elliptic equations, including degenerate cases.
We give sufficient conditions under which solutions of discretized in space second-order parabolic and elliptic equations, perhaps degenerate, admit estimates of the first derivatives in the space variables independent of the mesh size.