Approximation bounds for model reduction on polynomially mapped manifolds

HIGHLIGHTS

• What: The authors provide approximation bounds for ROMs on polynomially mapped manifolds. The authors show that the approximation bounds depend on the polynomial degree p of the mapping function as well as on the linear Kolmogorov n-width for the underlying problem. The authors are looking at Kolmogorov n-widths for a special type of submanifold for which the basis coefficients xqi are obtained from a polynomial of degree p ∈ N0. The authors show that these polynomially mapped manifolds are contained in a linear subspace, which leads to a lower and an upper bound for the polynomial . . .
  

   

  

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