  This work focuses on multidimensional summation-by-parts (SBP)
discretizations of linear elliptic operators with variable coefficients. We
consider a general SBP discretization with dense simultaneous approximation
terms (SATs), which serve as interior penalties to enforce boundary conditions
and inter-element coupling in a weak sense. Through the analysis of adjoint
consistency and stability, we present several conditions on the SAT penalties.
Based on these conditions, we generalize the modified scheme of Bassi and Rebay
(BR2) and the symmetric interior penalty Galerkin (SIPG) method to SBP-SAT
discretizations. Numerical experiments are carried out on unstructured grids
with triangular elements to verify the theoretical results.
