--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/+rv/+time/RungekuttaExteriorRvMg.m	Tue Jun 25 16:52:54 2019 +0200
@@ -0,0 +1,64 @@
+classdef RungekuttaExteriorRvMg < time.Timestepper
+    properties
+        F       % RHS of the ODE
+        k       % Time step
+        t       % Time point
+        v       % Solution vector
+        n       % Time level
+        rkScheme  % The particular RK scheme used for time integration
+        RV              % Residual Viscosity operator
+        DvDt            % Function for computing the time deriative used for the RV evaluation
+        v_unstable
+        viscosity
+    end
+    methods
+
+        function obj = RungekuttaExteriorRvMg(F, k, t0, v0, RV, DvDt, order)
+            obj.F = F;
+            obj.k = k;
+            obj.t = t0;
+            obj.v = v0;
+            obj.n = 0;
+            
+            if (order == 4) % Use specialized RK4 scheme
+                obj.rkScheme = @time.rk.rungekutta_4;
+            else
+                % Extract the coefficients for the specified order
+                % used for the RK updates from the Butcher tableua.
+                [s,a,b,c] = time.rk.butcherTableau(order);
+                coeffs = struct('s',s,'a',a,'b',b,'c',c);
+                obj.rkScheme = @(v,t,dt,F) time.rk.rungekutta(v, t , dt, F, coeffs);
+            end
+        
+            obj.RV = RV;
+            obj.DvDt = DvDt;
+            obj.v_unstable = 0*v0
+            obj.viscosity = 0*v0
+        end
+
+        function [v, t] = getV(obj)
+            v = obj.v;
+            t = obj.t;
+        end
+
+        function state = getState(obj)
+            dvdt = obj.DvDt(obj.v_unstable);
+            [viscosity, Df, firstOrderViscosity, residualViscosity] = obj.RV.evaluate(obj.v, dvdt);
+            state = struct('v', obj.v, 'dvdt', dvdt, 'Df', Df, 'viscosity', viscosity, 'residualViscosity', residualViscosity, 'firstOrderViscosity', firstOrderViscosity, 't', obj.t);
+        end
+
+        % Advances the solution vector one time step using the Runge-Kutta method given by
+        % obj.coeffs, using a fixed residual viscosity for the Runge-Kutta substeps
+        function obj = step(obj)            
+            % Fix the viscosity of the RHS function F
+            m = length(obj.viscosity);
+            F_stable = @(v,t) obj.F(v,t,spdiags(obj.viscosity,0,m,m));
+            F_unstable = @(v,t) obj.F(v,t,spdiags(0*obj.viscosity,0,m,m));
+            obj.v = obj.rkScheme(obj.v, obj.t, obj.k, F_stable);
+            obj.v_unstable = obj.rkScheme(obj.v, obj.t, obj.k, F_unstable);
+            obj.viscosity = obj.RV.evaluateViscosity(obj.v, obj.DvDt(obj.v_unstable));
+            obj.t = obj.t + obj.k;
+            obj.n = obj.n + 1;
+        end
+    end
+end
\ No newline at end of file

--- a/+rv/constructDiffOps.m	Tue Jun 25 15:04:53 2019 +0200
+++ b/+rv/constructDiffOps.m	Tue Jun 25 16:52:54 2019 +0200
@@ -5,7 +5,7 @@
     D_rv = @(v,Viscosity)(D(v) + D2(Viscosity)*v);
 
     %% DiffOps for residual viscosity
-    [D_flux, residualPenalties] = constructFluxDiffOp(scheme, g, residualOrder, schemeParams, opSet, BCs);
+    [D_res, residualPenalties] = constructFluxDiffOp(scheme, g, residualOrder, schemeParams, opSet, BCs);
     % TODO: Construct D_flux without closures when using bdfs.
     % diffOp = scheme(g, residualOrder, schemeParams{:}, opSet);
     % if ~isa(diffOp.D, 'function_handle')
@@ -16,7 +16,7 @@
 
     % DiffOp for flux in residual viscosity. Due to sign conventions of the implemented schemes, we need to
     % change the sign.
-    D_flux = @(v) -D_flux(v);
+    D_flux = @(v) -D_res(v);
     % DiffOp for time derivative in residual viscosity
     DvDt = D;
 end