Error estimates for asymptotic representations of integrals

Error Estimates for Lagrangian Flow Field Representations

Computing power outpaces I/O bandwidth in modern high performance computers, which leads to temporal sparsity in flow simulation data. Experiments show that Lagrangian flow representations (where pathlines are retrieved from short-time flow maps using interpolation and concatenation) outperform their Eulerian counterparts in advection tasks under these circumstances. Inspired by these results, ...

Some Error Estimates for the Numerical Approximation of Surface Integrals

Recently, the first author introduced a new approach to the numerical quadrature of surface integrals in the context of boundary element methods. It is assumed that a global parametrization m of the surface is only indirectly given (e.g., via an iterative method) and that m is not accessible analytically. Of particular interest are parametrizations which are based on automatic triangulations of...

Asymptotic Expansions for Integrals

Asymptotic Error Estimates for the Gauss Quadrature Formula

Estimates for Maximal Singular Integrals

It is shown that maximal truncations of nonconvolution L-bounded singular integral operators with kernels satisfying Hörmander’s condition are weak type (1, 1) and L bounded for 1 < p < ∞. Under stronger smoothness conditions, such estimates can be obtained using a generalization of Cotlar’s inequality. This inequality is not applicable here and the point of this article is to treat the bounded...