diff --git a/Project.toml b/Project.toml
index b605cb2c6b1..b2cc12010d2 100644
--- a/Project.toml
+++ b/Project.toml
@@ -61,7 +61,7 @@ TrixiConvexECOSExt = ["Convex", "ECOS"]
 [compat]
 CodeTracking = "1.0.5"
 ConstructionBase = "1.3"
-Convex = "0.15.4"
+Convex = "0.16"
 DataStructures = "0.18.15"
 DelimitedFiles = "1"
 DiffEqBase = "6 - 6.143"
diff --git a/ext/TrixiConvexECOSExt.jl b/ext/TrixiConvexECOSExt.jl
index fac127699ce..948dbf103cd 100644
--- a/ext/TrixiConvexECOSExt.jl
+++ b/ext/TrixiConvexECOSExt.jl
@@ -136,7 +136,7 @@ function Trixi.bisect_stability_polynomial(consistency_order, num_eig_vals,
                                            "reltol_inacc" => 5e-5,
                                            "nitref" => 9,
                                            "maxit" => 100,
-                                           "verbose" => 3); silent_solver = true)
+                                           "verbose" => 3); silent = true)
 
         abs_p = problem.optval
 
diff --git a/test/Project.toml b/test/Project.toml
index 5fc2bb18bdf..c8ae33a40ae 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -19,7 +19,7 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 [compat]
 Aqua = "0.8"
 CairoMakie = "0.10"
-Convex = "0.15.4"
+Convex = "0.16"
 DelimitedFiles = "1"
 Downloads = "1"
 ECOS = "1.1.2"
diff --git a/test/test_tree_1d_advection.jl b/test/test_tree_1d_advection.jl
index afa92efeddb..3885fb50061 100644
--- a/test/test_tree_1d_advection.jl
+++ b/test/test_tree_1d_advection.jl
@@ -84,8 +84,8 @@ end
 
 @trixi_testset "elixir_advection_perk2.jl" begin
     @test_trixi_include(joinpath(EXAMPLES_DIR, "elixir_advection_perk2.jl"),
-                        l2=[0.014139244532882265],
-                        linf=[0.019997568971592217])
+                        l2=[0.014139242834192841],
+                        linf=[0.01999756655819429])
     # Ensure that we do not have excessive memory allocations
     # (e.g., from type instabilities)
     let
diff --git a/test/test_unit.jl b/test/test_unit.jl
index de13d41e931..d7ec2084361 100644
--- a/test/test_unit.jl
+++ b/test/test_unit.jl
@@ -1662,16 +1662,16 @@ end
     ode_algorithm = Trixi.PairedExplicitRK2(12, tspan, vec(eig_vals))
 
     @test isapprox(ode_algorithm.a_matrix,
-                   [0.06453812656705388 0.02637096434203703
-                    0.09470601372266194 0.04165762264097442
-                    0.12332877820057538 0.05848940361760645
-                    0.1498701503275483 0.07740257694517898
-                    0.173421149536068 0.09930612319120471
-                    0.19261978147927503 0.12556203670254315
-                    0.2052334022622969 0.15840296137406676
-                    0.2073489042901963 0.2017420048007128
-                    0.19135142349998963 0.2631940310454649
-                    0.13942836392940833 0.3605716360705917], atol = 1e-13)
+                   [0.06453812656711647 0.02637096434197444
+                    0.09470601372274887 0.041657622640887494
+                    0.12332877820069793 0.058489403617483886
+                    0.14987015032771522 0.07740257694501203
+                    0.1734211495362651 0.0993061231910076
+                    0.19261978147948638 0.1255620367023318
+                    0.20523340226247055 0.1584029613738931
+                    0.20734890429023528 0.20174200480067384
+                    0.1913514234997008 0.26319403104575373
+                    0.13942836392866081 0.3605716360713392], atol = 1e-13)
 end
 
 @testset "Sutherlands Law" begin