diff --git a/include/ddc/chunk.hpp b/include/ddc/chunk.hpp
index a4137995a..b6115cfb9 100644
--- a/include/ddc/chunk.hpp
+++ b/include/ddc/chunk.hpp
@@ -449,7 +449,7 @@ class Chunk : public ChunkCommon<ElementType, SupportType, Kokkos::layout_right>
                 SupportType::rank() == (0 + ... + DElems::size()),
                 "Invalid number of dimensions");
         static_assert((is_discrete_element_v<DElems> && ...), "Expected DiscreteElements");
-        assert(this->m_domain.is_inside(delems...));
+        assert(this->m_domain.contains(delems...));
         return DDC_MDSPAN_ACCESS_OP(
                 this->m_allocation_mdspan,
                 detail::array(this->m_domain.distance_from_front(delems...)));
@@ -466,7 +466,7 @@ class Chunk : public ChunkCommon<ElementType, SupportType, Kokkos::layout_right>
                 SupportType::rank() == (0 + ... + DElems::size()),
                 "Invalid number of dimensions");
         static_assert((is_discrete_element_v<DElems> && ...), "Expected DiscreteElements");
-        assert(this->m_domain.is_inside(delems...));
+        assert(this->m_domain.contains(delems...));
         return DDC_MDSPAN_ACCESS_OP(
                 this->m_allocation_mdspan,
                 detail::array(this->m_domain.distance_from_front(delems...)));
diff --git a/include/ddc/chunk_span.hpp b/include/ddc/chunk_span.hpp
index 0f25f6dd9..0594dc9e3 100644
--- a/include/ddc/chunk_span.hpp
+++ b/include/ddc/chunk_span.hpp
@@ -603,7 +603,7 @@ class ChunkSpan : public ChunkCommon<ElementType, SupportType, LayoutStridedPoli
                 SupportType::rank() == (0 + ... + DElems::size()),
                 "Invalid number of dimensions");
         static_assert((is_discrete_element_v<DElems> && ...), "Expected DiscreteElements");
-        assert(this->m_domain.is_inside(delems...));
+        assert(this->m_domain.contains(delems...));
         return DDC_MDSPAN_ACCESS_OP(
                 this->m_allocation_mdspan,
                 detail::array(this->m_domain.distance_from_front(delems...)));
diff --git a/include/ddc/discrete_domain.hpp b/include/ddc/discrete_domain.hpp
index 98eb37877..7b3beca6f 100644
--- a/include/ddc/discrete_domain.hpp
+++ b/include/ddc/discrete_domain.hpp
@@ -194,7 +194,7 @@ class DiscreteDomain
     }
 
     template <class... DElems>
-    bool is_inside(DElems const&... delems) const noexcept
+    bool contains(DElems const&... delems) const noexcept
     {
         static_assert(
                 sizeof...(DDims) == (0 + ... + DElems::size()),
@@ -400,12 +400,12 @@ class DiscreteDomain<>
         return *this;
     }
 
-    static bool is_inside() noexcept
+    static bool contains() noexcept
     {
         return true;
     }
 
-    static bool is_inside(DiscreteElement<>) noexcept
+    static bool contains(DiscreteElement<>) noexcept
     {
         return true;
     }
diff --git a/include/ddc/storage_discrete_domain.hpp b/include/ddc/storage_discrete_domain.hpp
index 929197c33..79ba7fa32 100644
--- a/include/ddc/storage_discrete_domain.hpp
+++ b/include/ddc/storage_discrete_domain.hpp
@@ -274,7 +274,7 @@ class StorageDiscreteDomain
     // }
 
     template <class... DElems>
-    KOKKOS_FUNCTION bool is_inside(DElems const&... delems) const noexcept
+    KOKKOS_FUNCTION bool contains(DElems const&... delems) const noexcept
     {
         static_assert(
                 sizeof...(DDims) == (0 + ... + DElems::size()),
@@ -296,7 +296,7 @@ class StorageDiscreteDomain
                 sizeof...(DDims) == (0 + ... + DElems::size()),
                 "Invalid number of dimensions");
         static_assert((is_discrete_element_v<DElems> && ...), "Expected DiscreteElements");
-        assert(is_inside(delems...));
+        assert(contains(delems...));
         return DiscreteVector<DDims...>(
                 (detail::lower_bound(
                          get<DDims>(m_views).data(),
@@ -502,12 +502,12 @@ class StorageDiscreteDomain
 //         return *this;
 //     }
 
-//     static bool is_inside() noexcept
+//     static bool contains() noexcept
 //     {
 //         return true;
 //     }
 
-//     static bool is_inside(DiscreteElement<>) noexcept
+//     static bool contains(DiscreteElement<>) noexcept
 //     {
 //         return true;
 //     }
diff --git a/include/ddc/strided_discrete_domain.hpp b/include/ddc/strided_discrete_domain.hpp
index 74b3b4fec..2b2b793e9 100644
--- a/include/ddc/strided_discrete_domain.hpp
+++ b/include/ddc/strided_discrete_domain.hpp
@@ -219,7 +219,7 @@ class StridedDiscreteDomain
     // }
 
     template <class... DElems>
-    KOKKOS_FUNCTION bool is_inside(DElems const&... delems) const noexcept
+    KOKKOS_FUNCTION bool contains(DElems const&... delems) const noexcept
     {
         static_assert(
                 sizeof...(DDims) == (0 + ... + DElems::size()),
@@ -251,7 +251,7 @@ class StridedDiscreteDomain
                 sizeof...(DDims) == (0 + ... + DElems::size()),
                 "Invalid number of dimensions");
         static_assert((is_discrete_element_v<DElems> && ...), "Expected DiscreteElements");
-        assert(is_inside(delems...));
+        assert(contains(delems...));
         return DiscreteVector<DDims...>(
                 ((DiscreteElement<DDims>(take<DDims>(delems...))
                   - DiscreteElement<DDims>(m_element_begin))
@@ -455,12 +455,12 @@ class StridedDiscreteDomain<>
         return *this;
     }
 
-    static bool is_inside() noexcept
+    static bool contains() noexcept
     {
         return true;
     }
 
-    static bool is_inside(DiscreteElement<>) noexcept
+    static bool contains(DiscreteElement<>) noexcept
     {
         return true;
     }
diff --git a/tests/discrete_domain.cpp b/tests/discrete_domain.cpp
index 41b5908fc..c51ad4b78 100644
--- a/tests/discrete_domain.cpp
+++ b/tests/discrete_domain.cpp
@@ -248,8 +248,8 @@ TEST(DiscreteDomainTest, Remove)
 TEST(DiscreteDomainTest, IsInside)
 {
     DDomXY const dom_x_y(lbound_x_y, nelems_x_y);
-    EXPECT_TRUE(dom_x_y.is_inside(lbound_x_y));
-    EXPECT_FALSE(dom_x_y.is_inside(lbound_x_y + nelems_x_y));
+    EXPECT_TRUE(dom_x_y.contains(lbound_x_y));
+    EXPECT_FALSE(dom_x_y.contains(lbound_x_y + nelems_x_y));
 }
 
 TEST(DiscreteDomainTest, DistanceFromFront)
diff --git a/tests/storage_discrete_domain.cpp b/tests/storage_discrete_domain.cpp
index 6696deeb6..22845b7a2 100644
--- a/tests/storage_discrete_domain.cpp
+++ b/tests/storage_discrete_domain.cpp
@@ -97,5 +97,5 @@ TEST(StorageDiscreteDomainTest, Constructor)
     EXPECT_EQ(dom_xy.distance_from_front(lbound_x + 2, lbound_y + 0), DVectXY(1, 0));
     EXPECT_EQ(dom_xy.distance_from_front(lbound_x + 2, lbound_y + 2), DVectXY(1, 1));
     EXPECT_EQ(dom_xy.distance_from_front(lbound_x + 2, lbound_y + 5), DVectXY(1, 2));
-    EXPECT_FALSE(dom_xy.is_inside(lbound_x + 1, lbound_y + 0));
+    EXPECT_FALSE(dom_xy.contains(lbound_x + 1, lbound_y + 0));
 }
diff --git a/tests/strided_discrete_domain.cpp b/tests/strided_discrete_domain.cpp
index f4d8cb313..1792e3f42 100644
--- a/tests/strided_discrete_domain.cpp
+++ b/tests/strided_discrete_domain.cpp
@@ -260,8 +260,8 @@ TEST(StridedDiscreteDomainTest, Remove)
 TEST(StridedDiscreteDomainTest, IsInside)
 {
     DDomXY const dom_x_y(lbound_x_y, nelems_x_y, strides_x_y);
-    EXPECT_TRUE(dom_x_y.is_inside(lbound_x_y));
-    EXPECT_FALSE(dom_x_y.is_inside(lbound_x_y + DVectXY(1, 1)));
+    EXPECT_TRUE(dom_x_y.contains(lbound_x_y));
+    EXPECT_FALSE(dom_x_y.contains(lbound_x_y + DVectXY(1, 1)));
 }
 
 TEST(StridedDiscreteDomainTest, DistanceFromFront)