diff --git a/examples/dgmulti_1d/elixir_euler_shu_osher_gauss_shock_capturing.jl b/examples/dgmulti_1d/elixir_euler_shu_osher_gauss_shock_capturing.jl
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+++ b/examples/dgmulti_1d/elixir_euler_shu_osher_gauss_shock_capturing.jl
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+using Trixi
+using OrdinaryDiffEq
+
+γ_gas = 1.4
+equations = CompressibleEulerEquations1D(γ_gas)
+
+###############################################################################
+# setup the GSBP DG discretization that uses the Gauss operators from 
+# Chan, Del Rey Fernandez, Carpenter (2019). 
+# [https://doi.org/10.1137/18M1209234](https://doi.org/10.1137/18M1209234)
+
+# Shu-Osher initial condition for 1D compressible Euler equations
+# Example 8, https://www.sciencedirect.com/science/article/pii/0021999189902222
+function initial_condition_shu_osher(x, t, equations::CompressibleEulerEquations1D)
+    x0 = -4
+    
+    rho_left = 27/7
+    v_left = 4*sqrt(35)/9
+    p_left = 31/3
+    
+    # Replaced v_right = 0 to v_right = 0.1 to avoid positivity issues.
+    v_right = 0.1
+    p_right = 1.0
+    
+    rho = ifelse(x[1] > x0, 1 + 1/5*sin(5*x[1]), rho_left)
+    v = ifelse(x[1] > x0, v_right, v_left)
+    p = ifelse(x[1] > x0, p_right, p_left)
+
+    return prim2cons(SVector(rho + 0.1*rand(), v + 0.1*rand(), p + 0.1*rand()), equations)
+end
+
+initial_condition = initial_condition_shu_osher
+
+surface_flux = flux_lax_friedrichs
+volume_flux = flux_ranocha
+
+
+polydeg = 3
+basis = DGMultiBasis(Line(), polydeg, approximation_type = GaussSBP())
+
+indicator_sc = IndicatorHennemannGassner(equations, basis,
+                                         alpha_max = 0.5,
+                                         alpha_min = 0.001,
+                                         alpha_smooth = true,
+                                         variable = density_pressure)
+volume_integral = VolumeIntegralShockCapturingHG(indicator_sc;
+                                                 volume_flux_dg = volume_flux,
+                                                 volume_flux_fv = surface_flux)
+
+dg = DGMulti(basis,
+             surface_integral = SurfaceIntegralWeakForm(surface_flux),
+             volume_integral = volume_integral)
+
+
+boundary_condition = BoundaryConditionDirichlet(initial_condition)
+boundary_conditions = (; :entire_boundary => boundary_condition)
+
+###############################################################################
+#  setup the 1D mesh
+
+cells_per_dimension = (64,)
+mesh = DGMultiMesh(dg, cells_per_dimension,
+                   coordinates_min = (-5.0,), coordinates_max = (5.0,),
+                   periodicity = false)
+
+###############################################################################
+#  setup the semidiscretization and ODE problem
+
+semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, 
+                                    dg, boundary_conditions = boundary_conditions)
+
+tspan = (0.0, 2.0)
+ode = semidiscretize(semi, tspan)
+
+###############################################################################
+#  setup the callbacks
+
+# prints a summary of the simulation setup and resets the timers
+summary_callback = SummaryCallback()
+
+# analyse the solution in regular intervals and prints the results
+analysis_callback = AnalysisCallback(semi, interval = 100, uEltype = real(dg))
+
+# handles the re-calculation of the maximum Δt after each time step
+stepsize_callback = StepsizeCallback(cfl = 0.1)
+
+# collect all callbacks such that they can be passed to the ODE solver
+callbacks = CallbackSet(summary_callback, analysis_callback, stepsize_callback)
+
+# For future work, add PositivityPreservingLimiterZhangShu for DGMulti with Gauss nodes
+# stage_limiter! = PositivityPreservingLimiterZhangShu(thresholds=(5.0e-6, 5.0e-6),
+#                                                      variables=(Trixi.density, pressure))
+
+# ###############################################################################
+# # run the simulation
+
+sol = solve(ode, SSPRK43(), adaptive = true, callback = callbacks, save_everystep = true)
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