diff --git a/prototypes/CMakeLists.txt b/prototypes/CMakeLists.txt
index 560aae1ede..18011a0bda 100644
--- a/prototypes/CMakeLists.txt
+++ b/prototypes/CMakeLists.txt
@@ -1,6 +1,7 @@
 add_subdirectory(chorin_navier_stokes)
 add_subdirectory(direct_gls_navier_stokes)
 add_subdirectory(direct_steady_navier_stokes)
+add_subdirectory(kokkos_poisson)
 add_subdirectory(matrix_based_non_linear_poisson)
 add_subdirectory(matrix_free_non_linear_poisson)
 add_subdirectory(matrix_based_advection_diffusion)
diff --git a/prototypes/kokkos_poisson/CMakeLists.txt b/prototypes/kokkos_poisson/CMakeLists.txt
new file mode 100644
index 0000000000..d371d9b34f
--- /dev/null
+++ b/prototypes/kokkos_poisson/CMakeLists.txt
@@ -0,0 +1,2 @@
+add_executable(kokkos_poisson kokkos_poisson.cc)
+deal_ii_setup_target(kokkos_poisson)
diff --git a/prototypes/kokkos_poisson/kokkos_poisson.cc b/prototypes/kokkos_poisson/kokkos_poisson.cc
new file mode 100644
index 0000000000..e68240255d
--- /dev/null
+++ b/prototypes/kokkos_poisson/kokkos_poisson.cc
@@ -0,0 +1,351 @@
+/* ---------------------------------------------------------------------
+ *
+ * Copyright (C) 2024 by the Lethe authors
+ *
+ * This file is part of the Lethe library
+ *
+ * The Lethe library is free software; you can use it, redistribute
+ * it, and/or modify it under the terms of the GNU Lesser General
+ * Public License as published by the Free Software Foundation; either
+ * version 2.1 of the License, or (at your option) any later version.
+ * The full text of the license can be found in the file LICENSE at
+ * the top level of the Lethe distribution.
+ *
+ * A simple matrix-free solver for solving a vector Laplace problem
+ * using Kokkos via Portable::MatrixFree and Porable::FEEvaluation.
+ *
+ * ---------------------------------------------------------------------*/
+
+#include <deal.II/base/convergence_table.h>
+
+#include <deal.II/distributed/fully_distributed_tria.h>
+#include <deal.II/distributed/repartitioning_policy_tools.h>
+#include <deal.II/distributed/tria.h>
+
+#include <deal.II/dofs/dof_tools.h>
+
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_system.h>
+
+#include <deal.II/grid/grid_generator.h>
+
+#include <deal.II/lac/precondition.h>
+#include <deal.II/lac/solver_cg.h>
+
+#include <deal.II/matrix_free/cuda_fe_evaluation.h>
+#include <deal.II/matrix_free/cuda_matrix_free.h>
+#include <deal.II/matrix_free/fe_evaluation.h>
+#include <deal.II/matrix_free/matrix_free.h>
+
+#include <deal.II/numerics/data_out.h>
+#include <deal.II/numerics/vector_tools.h>
+
+using namespace dealii;
+
+static unsigned int counter = 0;
+
+template <int dim,
+          int fe_degree,
+          int n_components,
+          typename Number,
+          typename MemorySpace>
+class LaplaceOperator;
+
+template <int dim, int fe_degree, int n_components, typename Number>
+class LaplaceOperator<dim, fe_degree, n_components, Number, MemorySpace::Host>
+{
+public:
+  using VectorType =
+    LinearAlgebra::distributed::Vector<Number, MemorySpace::Host>;
+
+  LaplaceOperator() = default;
+
+  void
+  reinit(const Mapping<dim>              &mapping,
+         const DoFHandler<dim>           &dof_handler,
+         const AffineConstraints<Number> &constraints,
+         const Quadrature<1>             &quadrature)
+  {
+    typename MatrixFree<dim, Number>::AdditionalData additional_data;
+    additional_data.mapping_update_flags = update_gradients;
+
+    matrix_free.reinit(
+      mapping, dof_handler, constraints, quadrature, additional_data);
+  }
+
+  void
+  initialize_dof_vector(VectorType &vec) const
+  {
+    matrix_free.initialize_dof_vector(vec);
+  }
+
+  void
+  vmult(VectorType &dst, const VectorType &src) const
+  {
+    matrix_free.cell_loop(&LaplaceOperator::local_apply, this, dst, src, true);
+  }
+
+private:
+  void
+  local_apply(const MatrixFree<dim, Number>               &data,
+              VectorType                                  &dst,
+              const VectorType                            &src,
+              const std::pair<unsigned int, unsigned int> &cell_range) const
+  {
+    FEEvaluation<dim, fe_degree, fe_degree + 1, n_components, Number> phi(data);
+    for (unsigned int cell = cell_range.first; cell < cell_range.second; ++cell)
+      {
+        phi.reinit(cell);
+
+        phi.read_dof_values_plain(src);
+        phi.evaluate(EvaluationFlags::gradients);
+        for (unsigned int q = 0; q < phi.n_q_points; ++q)
+          phi.submit_gradient(phi.get_gradient(q), q);
+        phi.integrate(EvaluationFlags::gradients);
+        phi.distribute_local_to_global(dst);
+      }
+  }
+
+  MatrixFree<dim, Number> matrix_free;
+};
+
+
+
+template <int dim, int fe_degree, int n_components, typename Number>
+class LaplaceOperatorQuad
+{
+public:
+  DEAL_II_HOST_DEVICE void
+  operator()(CUDAWrappers::
+               FEEvaluation<dim, fe_degree, fe_degree + 1, n_components, Number>
+                      *fe_eval,
+             const int q_point) const
+  {
+    fe_eval->submit_gradient(fe_eval->get_gradient(q_point), q_point);
+  }
+};
+
+template <int dim, int fe_degree, int n_components, typename Number>
+class LaplaceOperatorLocal
+{
+public:
+  DEAL_II_HOST_DEVICE void
+  operator()(
+    const unsigned int                                          cell,
+    const typename CUDAWrappers::MatrixFree<dim, Number>::Data *gpu_data,
+    CUDAWrappers::SharedData<dim, Number>                      *shared_data,
+    const Number                                               *src,
+    Number                                                     *dst) const
+  {
+    (void)cell; // TODO?
+
+    CUDAWrappers::
+      FEEvaluation<dim, fe_degree, fe_degree + 1, n_components, Number>
+        fe_eval(
+          /*cell,*/ gpu_data, shared_data);
+    fe_eval.read_dof_values(src);
+    fe_eval.evaluate(false, true);
+    fe_eval.apply_for_each_quad_point(
+      LaplaceOperatorQuad<dim, fe_degree, n_components, Number>());
+    fe_eval.integrate(false, true);
+    fe_eval.distribute_local_to_global(dst);
+  }
+  static const unsigned int n_dofs_1d    = fe_degree + 1;
+  static const unsigned int n_local_dofs = Utilities::pow(fe_degree + 1, dim);
+  static const unsigned int n_q_points   = Utilities::pow(fe_degree + 1, dim);
+};
+
+template <int dim, int fe_degree, int n_components, typename Number>
+class LaplaceOperator<dim,
+                      fe_degree,
+                      n_components,
+                      Number,
+                      MemorySpace::Default>
+{
+public:
+  using VectorType =
+    LinearAlgebra::distributed::Vector<Number, MemorySpace::Default>;
+
+  LaplaceOperator() = default;
+
+  void
+  reinit(const Mapping<dim>              &mapping,
+         const DoFHandler<dim>           &dof_handler,
+         const AffineConstraints<Number> &constraints,
+         const Quadrature<1>             &quadrature)
+  {
+    typename CUDAWrappers::MatrixFree<dim, Number>::AdditionalData
+      additional_data;
+    additional_data.mapping_update_flags = update_JxW_values | update_gradients;
+
+    matrix_free.reinit(
+      mapping, dof_handler, constraints, quadrature, additional_data);
+  }
+
+  void
+  initialize_dof_vector(VectorType &vec) const
+  {
+    matrix_free.initialize_dof_vector(vec);
+  }
+
+  void
+  vmult(VectorType &dst, const VectorType &src) const
+  {
+    dst = 0.0; // TODO: annoying
+    LaplaceOperatorLocal<dim, fe_degree, n_components, Number> local_operator;
+    matrix_free.cell_loop(local_operator, src, dst);
+    matrix_free.copy_constrained_values(src, dst); // TODO: annoying
+  }
+
+private:
+  CUDAWrappers::MatrixFree<dim, Number> matrix_free;
+};
+
+
+
+template <int dim, typename T>
+class AnalyticalFunction : public Function<dim, T>
+{
+public:
+  AnalyticalFunction(const unsigned int n_components)
+    : Function<dim, T>(n_components)
+  {}
+
+  virtual T
+  value(const Point<dim, T> &p, const unsigned int component = 0) const override
+  {
+    double temp = 0.0;
+
+    for (unsigned int d = 0; d < dim; ++d)
+      temp += std::sin(p[d]);
+
+    return temp * (1.0 + component);
+  }
+};
+
+
+
+template <unsigned int dim,
+          const int    degree,
+          int          n_components,
+          typename MemorySpace>
+void
+run(const unsigned int n_refinements, ConvergenceTable &table)
+{
+  const MPI_Comm comm = MPI_COMM_WORLD;
+
+  using Number     = double;
+  using VectorType = LinearAlgebra::distributed::Vector<Number, MemorySpace>;
+
+  parallel::distributed::Triangulation<dim> tria(comm);
+
+  GridGenerator::hyper_cube(tria);
+  tria.refine_global(n_refinements);
+
+  const MappingQ1<dim> mapping;
+  const FE_Q<dim>      fe_q(degree);
+  const FESystem<dim>  fe(fe_q, n_components);
+  const QGauss<dim>    quadrature(degree + 1);
+
+  DoFHandler<dim> dof_handler(tria);
+  dof_handler.distribute_dofs(fe);
+
+  AffineConstraints<Number> constraints;
+  DoFTools::make_zero_boundary_constraints(dof_handler, constraints);
+  constraints.close();
+
+  LaplaceOperator<dim, degree, n_components, Number, MemorySpace>
+    laplace_operator;
+
+  laplace_operator.reinit(mapping,
+                          dof_handler,
+                          constraints,
+                          quadrature.get_tensor_basis()[0]);
+
+  VectorType src, dst;
+
+  laplace_operator.initialize_dof_vector(src);
+  laplace_operator.initialize_dof_vector(dst);
+
+  {
+    LinearAlgebra::distributed::Vector<Number> src_host(src.get_partitioner());
+
+    VectorTools::create_right_hand_side<dim, dim>(
+      mapping,
+      dof_handler,
+      quadrature,
+      AnalyticalFunction<dim, Number>(n_components),
+      src_host,
+      constraints);
+
+    LinearAlgebra::ReadWriteVector<Number> rw_vector(
+      src.get_partitioner()->locally_owned_range());
+    rw_vector.import(src_host, VectorOperation::insert);
+    src.import(rw_vector, VectorOperation::insert);
+
+    dst = 0.0;
+  }
+
+  PreconditionIdentity preconditioner;
+
+  ReductionControl     solver_control;
+  SolverCG<VectorType> solver(solver_control);
+  solver.solve(laplace_operator, dst, src, preconditioner);
+
+  {
+    LinearAlgebra::distributed::Vector<Number> dst_host(dst.get_partitioner());
+
+    LinearAlgebra::ReadWriteVector<Number> rw_vector(
+      src.get_partitioner()->locally_owned_range());
+    rw_vector.import(dst, VectorOperation::insert);
+    dst_host.import(rw_vector, VectorOperation::insert);
+
+    std::string file_name = "solution_" + std::to_string(counter++) + ".vtu";
+
+    DataOut<dim> data_out;
+
+    DataOutBase::VtkFlags flags;
+    flags.write_higher_order_cells = true;
+    data_out.set_flags(flags);
+
+    data_out.attach_dof_handler(dof_handler);
+    data_out.add_data_vector(dst_host, "solution");
+    data_out.build_patches(mapping,
+                           degree + 1,
+                           DataOut<dim>::CurvedCellRegion::curved_inner_cells);
+    data_out.write_vtu_in_parallel(file_name, MPI_COMM_WORLD);
+  }
+
+  table.add_value("fe_degree", degree);
+  table.add_value("n_refinements", n_refinements);
+  table.add_value("n_components", n_components);
+  table.add_value("n_dofs", dof_handler.n_dofs());
+
+  if (std::is_same_v<MemorySpace, dealii::MemorySpace::Host>)
+    table.add_value("version", "host");
+  else
+    table.add_value("version", "default");
+
+  table.add_value("norm", dst.l2_norm());
+}
+
+int
+main(int argc, char **argv)
+{
+  Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv, 1);
+
+  const unsigned int dim           = 2;
+  const unsigned int fe_degree     = 3;
+  unsigned int       n_refinements = 3;
+
+  ConvergenceTable table;
+
+  run<dim, fe_degree, 1, MemorySpace::Host>(n_refinements, table);
+  run<dim, fe_degree, 1, MemorySpace::Default>(n_refinements, table);
+  run<dim, fe_degree, dim, MemorySpace::Host>(n_refinements, table);
+  run<dim, fe_degree, dim, MemorySpace::Default>(n_refinements, table);
+  run<dim, fe_degree, dim + 1, MemorySpace::Host>(n_refinements, table);
+  run<dim, fe_degree, dim + 1, MemorySpace::Default>(n_refinements, table);
+
+  table.write_text(std::cout);
+}