Accurate solution-adaptive finite difference schemes for coarse and fine grids

• We introduce solution dependent finite difference stencils whose coefficients adapt to the current numerical solution by minimizing the truncation error in the least squares sense. The resulting scheme has the resolution capacity of dispersion relation preserving difference stencils in under-resolved domains, together with the high order convergence rate of conventional central difference methods in well resolved regions. Numerical experiments reveal that the new stencils outperform their conventional counterparts on all grid resolutions from very coarse to very fine.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Keyword

Adaptivity

Finite differences

Least squares

Dispersion relation preserving

Accuracy

Convergence

Accuracy

Adaptivity

Convergence

Dispersion relation preserving

Finite differences

Least squares

Publication and Content Type

ref (subject category)

art (subject category)