  A novel approach for selecting appropriate reconstructions is implemented to
the hyperbolic conservation laws in the high-order local polynomial-based
framework, e.g., the discontinuous Galerkin (DG) and flux reconstruction (FR)
schemes. The high-order polynomial approximation generally fails to correctly
capture a strong discontinuity inside a cell due to the Runge phenomenon, which
is replaced by more stable approximation on the basis of a troubled-cell
indicator such as that used in the total variation bounded (TVB) limiter. This
paper examines the applicability of a new algorithm, so-called boundary
variation diminishing (BVD) reconstruction, to the weighted essentially
non-oscillatory (WENO) methodology in the FR framework including the nodal type
DG method. The BVD reconstruction adaptively chooses a proper approximation for
the solution function so as to minimize the jump between values at the left-
and right-side of cell boundaries without any ad hoc constant such as the TVB
parameter. Several numerical tests are conducted for a linear advection
equation as well as the selection of an appropriate reconstruction, where the
results of the BVD algorithm are comparable to those using the conventional TVB
limiter. Note that the present work is limited to third or lower order
polynomials, leaving the implementations for higher-order schemes a future
work.
