diff --git a/src/analysis/Polynomial1D.hpp b/src/analysis/Polynomial1D.hpp
index 20d4cf90ac11c8b0ae6c264b9f3ccf632d0c493e..894ffa8d8c03bb58f2389fc1b02917b181c759c5 100644
--- a/src/analysis/Polynomial1D.hpp
+++ b/src/analysis/Polynomial1D.hpp
@@ -202,14 +202,14 @@ class [[nodiscard]] Polynomial1D
   PUGS_INLINE
   double& coefficient(const size_t i)
   {
-    Assert(i < m_coefficients.size());
+    Assert(i < m_coefficients.size(), "invalid coefficient number");
     return m_coefficients[i];
   }
 
   PUGS_INLINE
   const double& coefficient(const size_t i) const
   {
-    Assert(i < m_coefficients.size());
+    Assert(i < m_coefficients.size(), "invalid coefficient number");
     return m_coefficients[i];
   }
 
diff --git a/tests/test_Polynomial1D.cpp b/tests/test_Polynomial1D.cpp
index 110cfadf74bad94ce8a1e8fc3ff6dff8247cad3f..cecd35b3697bedcd4664a9ea313091adab78d24b 100644
--- a/tests/test_Polynomial1D.cpp
+++ b/tests/test_Polynomial1D.cpp
@@ -254,6 +254,15 @@ TEST_CASE("Polynomial1D", "[analysis]")
   }
 
 #ifndef NDEBUG
-  SECTION("checking for bounds validation") {}
+  SECTION("checking for bounds validation")
+  {
+    Polynomial1D p({-1, 0, 0, 1});
+    REQUIRE_THROWS_AS(p.coefficient(4), AssertError);
+
+    const Polynomial1D q({-1, 0, 0, 1});
+    REQUIRE_THROWS_AS(q.coefficient(4), AssertError);
+
+    REQUIRE_THROWS_AS(Polynomial1D{std::vector<double>{}}, AssertError);
+  }
 #endif   // NDEBUG
 }