--- a/+sbp/InterpOpsMC.m	Thu Dec 06 10:32:02 2018 +0100
+++ b/+sbp/InterpOpsMC.m	Fri Dec 07 11:10:31 2018 -0800
@@ -1,3 +1,19 @@
+% Interpolation operators by Mattsson and Carpenter (MC), see
+% Mattsson and Carpenter,
+% "Stable and Accurate Interpolatino Operators for High-Order Multiblock Finite DIfference Methods",
+% https://epubs.siam.org/doi/pdf/10.1137/090750068
+%
+% Let ^* denote the adjoint. These operators satsify
+%
+% Iuv2 = Iv2u^*
+%
+% Both Iu2v and Iv2u have p:th order accuracy, if the interior stencil is
+% of order 2p.
+%
+% This approach leads to a reduction of the convergence rate by one order for
+% PDEs with 2nd derivatives in space, as compared to conforming interfaces.
+% To obtain full convergence rate, use the order-preserving (OP) operators in
+% InterpOpsOP.m
 classdef InterpOpsMC < sbp.InterpOps
     properties
 

--- a/+sbp/InterpOpsOP.m	Thu Dec 06 10:32:02 2018 +0100
+++ b/+sbp/InterpOpsOP.m	Fri Dec 07 11:10:31 2018 -0800
@@ -1,3 +1,21 @@
+% Order-preserving (OP) interpolation operators, see
+% Almquist, Wang, Werpers,
+% "Order-Preserving Interpolation for Summation-by-Parts Operators
+% at Non-Conforming Interfaces", https://arxiv.org/abs/1806.01931
+%
+% Let ^* denote the adjoint. These operators satsify
+%
+% Iuv2.good = Iv2u.bad^*
+% Iv2u.good = Iu2v.bad^*
+%
+% The .bad operators have the same order of accuracy as the operators
+% by Mattsson and Carpenter (MC) in InterpOpsMC, i.e. order p,
+% if the interior stencil is order 2p. The .good operators are
+% one order more accurate, i.e. order p+1.
+%
+% For PDEs of second order in space, the OP operators allow for the same
+% convergence rate as with conforming interfaces, which is an improvement
+% by one order compared what is possible with the MC operators.
 classdef InterpOpsOP < sbp.InterpOps
     properties