diff --git a/README.md b/README.md
index c177ad2347f..673708d8b89 100644
--- a/README.md
+++ b/README.md
@@ -7,6 +7,7 @@
 [![Build Status](https://github.com/trixi-framework/Trixi.jl/workflows/CI/badge.svg)](https://github.com/trixi-framework/Trixi.jl/actions?query=workflow%3ACI)
 [![Codecov](https://codecov.io/gh/trixi-framework/Trixi.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/trixi-framework/Trixi.jl)
 [![Coveralls](https://coveralls.io/repos/github/trixi-framework/Trixi.jl/badge.svg?branch=main)](https://coveralls.io/github/trixi-framework/Trixi.jl?branch=main)
+[![Aqua QA](https://raw.githubusercontent.com/JuliaTesting/Aqua.jl/master/badge.svg)](https://github.com/JuliaTesting/Aqua.jl)
 [![License: MIT](https://img.shields.io/badge/License-MIT-success.svg)](https://opensource.org/licenses/MIT)
 [![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.3996439.svg)](https://doi.org/10.5281/zenodo.3996439)
 [![Downloads](https://shields.io/endpoint?url=https://pkgs.genieframework.com/api/v1/badge/Trixi)](https://pkgs.genieframework.com?packages=Trixi)
diff --git a/docs/src/index.md b/docs/src/index.md
index bb2afd1019f..9ffaee26c40 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -7,6 +7,7 @@
 [![Build Status](https://github.com/trixi-framework/Trixi.jl/workflows/CI/badge.svg)](https://github.com/trixi-framework/Trixi.jl/actions?query=workflow%3ACI)
 [![Codecov](https://codecov.io/gh/trixi-framework/Trixi.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/trixi-framework/Trixi.jl)
 [![Coveralls](https://coveralls.io/repos/github/trixi-framework/Trixi.jl/badge.svg?branch=main)](https://coveralls.io/github/trixi-framework/Trixi.jl?branch=main)
+[![Aqua QA](https://raw.githubusercontent.com/JuliaTesting/Aqua.jl/master/badge.svg)](https://github.com/JuliaTesting/Aqua.jl)
 [![License: MIT](https://img.shields.io/badge/License-MIT-success.svg)](https://opensource.org/licenses/MIT)
 [![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.3996439.svg)](https://doi.org/10.5281/zenodo.3996439)
 
diff --git a/test/Project.toml b/test/Project.toml
index 7115a19b441..c45be49a5d0 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -1,13 +1,5 @@
-[compat]
-BSON = "0.3.3"
-CairoMakie = "0.6, 0.7, 0.8, 0.9, 0.10"
-Flux = "0.13 - 0.13.12" # TODO: Return to "0.13" once https://github.com/FluxML/Flux.jl/issues/2204 is resolved
-ForwardDiff = "0.10"
-MPI = "0.20"
-OrdinaryDiffEq = "6.49.1"
-Plots = "1.16"
-
 [deps]
+Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
 BSON = "fbb218c0-5317-5bc6-957e-2ee96dd4b1f0"
 CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
 Downloads = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
@@ -21,6 +13,16 @@ Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
+[compat]
+Aqua = "0.7"
+BSON = "0.3.3"
+CairoMakie = "0.6, 0.7, 0.8, 0.9, 0.10"
+Flux = "0.13.15, 0.14"
+ForwardDiff = "0.10"
+MPI = "0.20"
+OrdinaryDiffEq = "6.49.1"
+Plots = "1.16"
+
 [preferences.OrdinaryDiffEq]
 PrecompileAutoSpecialize = false
 PrecompileAutoSwitch = false
diff --git a/test/runtests.jl b/test/runtests.jl
index f1adbaaf1df..7e195fe7402 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -109,6 +109,7 @@ const TRIXI_NTHREADS = clamp(Sys.CPU_THREADS, 2, 3)
 
     @time if TRIXI_TEST == "all" || TRIXI_TEST == "misc_part2"
         include("test_special_elixirs.jl")
+        include("test_aqua.jl")
     end
 
     @time if TRIXI_TEST == "all" || TRIXI_TEST == "performance_specializations_part1"
diff --git a/test/test_aqua.jl b/test/test_aqua.jl
new file mode 100644
index 00000000000..f7ab4f545d0
--- /dev/null
+++ b/test/test_aqua.jl
@@ -0,0 +1,18 @@
+module TestAqua
+
+using Aqua
+using Test
+using Trixi
+
+include("test_trixi.jl")
+
+@timed_testset "Aqua.jl" begin
+    Aqua.test_all(Trixi,
+                  ambiguities = false,
+                  # exceptions necessary for adding a new method `StartUpDG.estimate_h`
+                  # in src/solvers/dgmulti/sbp.jl
+                  piracy = (treat_as_own = [Trixi.StartUpDG.RefElemData,
+                                            Trixi.StartUpDG.MeshData],))
+end
+
+end #module
diff --git a/test/test_tree_2d_euler.jl b/test/test_tree_2d_euler.jl
index e1e3ad32e7d..1b8a261a60d 100644
--- a/test/test_tree_2d_euler.jl
+++ b/test/test_tree_2d_euler.jl
@@ -140,7 +140,7 @@ EXAMPLES_DIR = pkgdir(Trixi, "examples", "tree_2d_dgsem")
   @trixi_testset "elixir_euler_sedov_blast_wave_neuralnetwork_perssonperaire.jl" begin
     @test_trixi_include(joinpath(EXAMPLES_DIR, "elixir_euler_sedov_blast_wave_neuralnetwork_perssonperaire.jl"),
       l2   = [0.0845430093623868, 0.09271459184623232, 0.09271459184623232, 0.4377291875101709],
-      linf = [1.3608553480069898, 1.6822884847136004, 1.6822884847135997, 4.220147414536653],
+      linf = [1.3608553480069898, 1.6822884847136004, 1.6822884847135997, 4.2201475428867035],
       maxiters = 30,
       coverage_override = (maxiters=6,))
   end