diff --git a/CHANGELOG.md b/CHANGELOG.md
index 62dad742..aa8b5d39 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -5,6 +5,17 @@ All notable changes to this project will be documented in this file.
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
+## [0.5.3] - 2024-08-16
+
+### Fixed
+- Typo: `node_coorinates_unit_cube` -> `node_coordinates_unit_cube`.
+- Bug in `nullspace_linear_elasticity`.
+- Bug in `PVector` when working in split format.
+
+### Deprecated
+
+- `near_nullspace_linear_elasticity` in favor of `nullspace_linear_elasticity`.
+
 ## [0.5.2] - 2024-08-13
 
 ### Added
diff --git a/Project.toml b/Project.toml
index 49939155..73c8b770 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "PartitionedArrays"
 uuid = "5a9dfac6-5c52-46f7-8278-5e2210713be9"
 authors = ["Francesc Verdugo <f.verdugo.rojano@vu.nl> and contributors"]
-version = "0.5.2"
+version = "0.5.3"
 
 [deps]
 CircularArrays = "7a955b69-7140-5f4e-a0ed-f168c5e2e749"
diff --git a/src/PartitionedArrays.jl b/src/PartitionedArrays.jl
index 5575613c..eef27803 100644
--- a/src/PartitionedArrays.jl
+++ b/src/PartitionedArrays.jl
@@ -180,7 +180,9 @@ include("p_timer.jl")
 export laplacian_fdm
 export laplacian_fem
 export linear_elasticity_fem
-export node_coorinates_unit_cube
+export node_coordinates_unit_cube
+export nullspace_linear_elasticity
+export nullspace_linear_elasticity!
 export near_nullspace_linear_elasticity
 include("gallery.jl")
 
diff --git a/src/gallery.jl b/src/gallery.jl
index 231dcce1..f68fec9d 100644
--- a/src/gallery.jl
+++ b/src/gallery.jl
@@ -415,12 +415,12 @@ function node_to_dof_partition(node_partition,D)
     dof_partition
 end
 
-function node_coorinates_unit_cube(
+function node_coordinates_unit_cube(
         nodes_per_dir, # free (== interior) nodes
         parts_per_dir,
         parts,
         ;
-        split_format = Val(true),
+        split_format = Val(false),
         value_type::Type{Tv} = Float64,) where Tv
 
     function setup!(own_x,mynodes)
@@ -443,7 +443,12 @@ function node_coorinates_unit_cube(
     x
 end
 
-function near_nullspace_linear_elasticity(x,
+function near_nullspace_linear_elasticity(a...;b...)
+    @warn "near_nullspace_linear_elasticity is deprecated, use nullspace_linear_elasticity instead"
+    nullspace_linear_elasticity(a...;b...)
+end
+
+function nullspace_linear_elasticity(x,
         row_partition = node_to_dof_partition(partition(axes(x,1)),length(eltype(x)))
     )
     T = eltype(x)
@@ -461,10 +466,10 @@ function near_nullspace_linear_elasticity(x,
     dof_partition = row_partition
     split_format = Val(eltype(partition(x)) <: SplitVector)
     B = [ pzeros(Tv,dof_partition;split_format) for _ in 1:nb ]
-    near_nullspace_linear_elasticity!(B,x)
+    nullspace_linear_elasticity!(B,x)
 end
 
-function near_nullspace_linear_elasticity!(B,x)
+function nullspace_linear_elasticity!(B,x)
     D = length(eltype(x))
     if D == 1
         foreach(own_values(B[1])) do own_b
diff --git a/src/p_vector.jl b/src/p_vector.jl
index ca7a7fac..ea75e03c 100644
--- a/src/p_vector.jl
+++ b/src/p_vector.jl
@@ -527,6 +527,7 @@ struct SplitVectorAssemblyCache{A,B,C,D}
     buffer_snd::C # NB
     buffer_rcv::C
     exchange_setup::D
+    reversed::Bool
 end
 function Base.reverse(a::SplitVectorAssemblyCache)
     SplitVectorAssemblyCache(
@@ -537,6 +538,7 @@ function Base.reverse(a::SplitVectorAssemblyCache)
                     a.buffer_rcv,
                     a.buffer_snd,
                     a.exchange_setup,
+                    !(a.reversed),
                    )
 end
 function copy_cache(a::SplitVectorAssemblyCache)
@@ -549,23 +551,29 @@ function copy_cache(a::SplitVectorAssemblyCache)
                     a.own_indices_rcv,
                     buffer_snd,
                     buffer_rcv,
-                    a.exchange_setup
+                    a.exchange_setup,
+                    a.reversed,
                    )
 end
 
 function p_vector_cache_impl(::Type{<:SplitVector},vector_partition,index_partition)
     neighbors_snd,neighbors_rcv= assembly_neighbors(index_partition)
     indices_snd,indices_rcv = assembly_local_indices(index_partition,neighbors_snd,neighbors_rcv)
-    map(indices_snd,indices_rcv,index_partition) do ids_snd,ids_rcv,myids
+    ghost_indices_snd = map(indices_snd) do ids
+        JaggedArray(copy(ids.data),ids.ptrs)
+    end
+    own_indices_rcv = map(indices_rcv) do ids
+        JaggedArray(copy(ids.data),ids.ptrs)
+    end
+    foreach(ghost_indices_snd,own_indices_rcv,index_partition) do ids_snd,ids_rcv,myids
         map_local_to_ghost!(ids_snd.data,myids)
         map_local_to_own!(ids_rcv.data,myids)
     end
-    ghost_indices_snd = indices_snd
-    own_indices_rcv = indices_rcv
-    buffers_snd,buffers_rcv = map(assembly_buffers,vector_partition,indices_snd,indices_rcv) |> tuple_of_arrays
+    buffers_snd,buffers_rcv = map(assembly_buffers,vector_partition,ghost_indices_snd,own_indices_rcv) |> tuple_of_arrays
     graph = ExchangeGraph(neighbors_snd,neighbors_rcv)
     exchange_setup = setup_exchange(buffers_rcv,buffers_snd,graph)
-    SplitVectorAssemblyCache(neighbors_snd,neighbors_rcv,ghost_indices_snd,own_indices_rcv,buffers_snd,buffers_rcv,exchange_setup)
+    reversed = false
+    SplitVectorAssemblyCache(neighbors_snd,neighbors_rcv,ghost_indices_snd,own_indices_rcv,buffers_snd,buffers_rcv,exchange_setup,reversed)
 end
 
 function p_vector_cache_impl(::Type{<:SplitVector{<:JaggedArray}},vector_partition,index_partition)
@@ -610,6 +618,7 @@ function assemble_impl!(f,vector_partition,cache::JaggedArrayAssemblyCache)
 end
 
 function assemble_impl!(f,vector_partition,cache::SplitVectorAssemblyCache)
+    reversed = cache.reversed
     ghost_indices_snd=cache.ghost_indices_snd
     own_indices_rcv=cache.own_indices_rcv
     neighbors_snd=cache.neighbors_snd
@@ -618,7 +627,11 @@ function assemble_impl!(f,vector_partition,cache::SplitVectorAssemblyCache)
     buffer_rcv=cache.buffer_rcv
     exchange_setup=cache.exchange_setup
     foreach(vector_partition,ghost_indices_snd,buffer_snd) do values,ghost_indices_snd,buffer_snd
-        ghost_vals = values.blocks.ghost
+        if reversed
+            ghost_vals = values.blocks.own
+        else
+            ghost_vals = values.blocks.ghost
+        end
         for (p,hid) in enumerate(ghost_indices_snd.data)
             buffer_snd.data[p] = ghost_vals[hid]
         end
@@ -629,7 +642,11 @@ function assemble_impl!(f,vector_partition,cache::SplitVectorAssemblyCache)
     @fake_async begin
         wait(t)
         foreach(vector_partition,own_indices_rcv,buffer_rcv) do values,own_indices_rcv,buffer_rcv
-            own_vals = values.blocks.own
+            if reversed
+                own_vals = values.blocks.ghost
+            else
+                own_vals = values.blocks.own
+            end
             for (p,oid) in enumerate(own_indices_rcv.data)
                 own_vals[oid] = f(own_vals[oid],buffer_rcv.data[p])
             end
diff --git a/test/gallery_tests.jl b/test/gallery_tests.jl
index 07fb9a13..20c4905a 100644
--- a/test/gallery_tests.jl
+++ b/test/gallery_tests.jl
@@ -32,20 +32,44 @@ function gallery_tests(distribute,parts_per_dir)
     @test isa(y,PVector)
     A = psparse(SparseMatrixCSR{1,Float64,Int32},args...) |> fetch
     A |> centralize |> display
-    Y = A*pones(axes(A,2))
+    y = A*pones(axes(A,2))
     @test isa(y,PVector)
 
     args = linear_elasticity_fem(nodes_per_dir,parts_per_dir,ranks)
     A = psparse(args...) |> fetch
     A |> centralize |> display
-    Y = A*pones(axes(A,2))
+    y = A*pones(axes(A,2))
     @test isa(y,PVector)
 
-    x = node_coorinates_unit_cube(nodes_per_dir,parts_per_dir,ranks)
-    B = near_nullspace_linear_elasticity(x)
+    x = node_coordinates_unit_cube(nodes_per_dir,parts_per_dir,ranks)
+    B = nullspace_linear_elasticity(x)
     @test isa(B[1],PVector)
-    B = near_nullspace_linear_elasticity(x,partition(axes(A,2)))
+    y = A*pones(axes(A,2))
+    @test isa(y,PVector)
+    B = nullspace_linear_elasticity(x,partition(axes(A,2)))
     @test isa(B[1],PVector)
+    y = A*pones(axes(A,2))
+    @test isa(Y,PVector)
+    y = A*B[1]
+    @test isa(y,PVector)
+    nullspace_linear_elasticity!(B,x)
+    y = A*B[1]
+    @test isa(y,PVector)
+
+    x = node_coordinates_unit_cube(nodes_per_dir,parts_per_dir,ranks,split_format=true)
+    B = nullspace_linear_elasticity(x)
+    @test isa(B[1],PVector)
+    y = A*pones(axes(A,2))
+    @test isa(y,PVector)
+    B = nullspace_linear_elasticity(x,partition(axes(A,2)))
+    @test isa(B[1],PVector)
+    y = A*pones(axes(A,2))
+    @test isa(Y,PVector)
+    y = A*B[1]
+    @test isa(y,PVector)
+    nullspace_linear_elasticity!(B,x)
+    y = A*B[1]
+    @test isa(y,PVector)
 
 end