  Convolving the output of Discontinuous Galerkin (DG) computations using
spline filters can improve both smoothness and accuracy of the output. At
domain boundaries, these filters have to be one-sided. Recently,
position-dependent smoothness-increasing accuracy-preserving (PSIAC) filters
were shown to be a superset of the top-of-the-line one-sided RLKV and SRV
filters. Since PSIAC filters can be formulated symbolically, convolution with
PSIAC filters reduces to a stable inner product with the DG output and hence
provides a stable and efficient implementation.
  The paper focuses on the remarkable fact that, for the canonical linear or
non-linear hyperbolic test equation, new piecewise constant PSIAC filters of
small support outperform the top-of-the-line boundary filters in the
literature. These least-degree filters reduce the error at the boundaries to
less than the error even of the symmetric filters of the same support that are
applied in the interior . Due to their simplicity, and since this least degree
filter has an exact symbolic form, convolution is stable as well as efficient
and derivatives of the convolved output are easy to compute.
