diff --git a/CHANGELOG.md b/CHANGELOG.md
index dde65eed1..ffd77754d 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -21,6 +21,7 @@
 
 ## Bug fixes
 
+-   Correct a sign error in Dirichlet boundary conditions in the Finite Element Method ([#706](https://github.com/pybamm-team/PyBaMM/pull/706))
 -   Pass the correct dimensional temperature to open circuit potential ([#702](https://github.com/pybamm-team/PyBaMM/pull/702))
 -   Adds missing temperature dependence in electrolyte and interface submodels ([#698](https://github.com/pybamm-team/PyBaMM/pull/698))
 -   Fix differentiation of functions that have more than one argument ([#687](https://github.com/pybamm-team/PyBaMM/pull/687))
diff --git a/pybamm/spatial_methods/scikit_finite_element.py b/pybamm/spatial_methods/scikit_finite_element.py
index ddf501049..464a1d68a 100644
--- a/pybamm/spatial_methods/scikit_finite_element.py
+++ b/pybamm/spatial_methods/scikit_finite_element.py
@@ -51,11 +51,11 @@ class ScikitFiniteElement(pybamm.SpatialMethod):
         symbol_mesh = self.mesh
         if symbol.name == "y":
             vector = pybamm.Vector(
-                symbol_mesh["current collector"][0].edges["y"], domain=symbol.domain
+                symbol_mesh["current collector"][0].coordinates[0, :][:, np.newaxis]
             )
         elif symbol.name == "z":
             vector = pybamm.Vector(
-                symbol_mesh["current collector"][0].edges["z"], domain=symbol.domain
+                symbol_mesh["current collector"][0].coordinates[1, :][:, np.newaxis]
             )
         else:
             raise pybamm.GeometryError(
@@ -121,7 +121,7 @@ class ScikitFiniteElement(pybamm.SpatialMethod):
             # set Dirichlet value at facets corresponding to tab
             neg_bc_load = np.zeros(mesh.npts)
             neg_bc_load[mesh.negative_tab_dofs] = 1
-            boundary_load = boundary_load - neg_bc_value * pybamm.Vector(neg_bc_load)
+            boundary_load = boundary_load + neg_bc_value * pybamm.Vector(neg_bc_load)
         else:
             raise ValueError(
                 "boundary condition must be Dirichlet or Neumann, not '{}'".format(
@@ -138,7 +138,7 @@ class ScikitFiniteElement(pybamm.SpatialMethod):
             # set Dirichlet value at facets corresponding to tab
             pos_bc_load = np.zeros(mesh.npts)
             pos_bc_load[mesh.positive_tab_dofs] = 1
-            boundary_load = boundary_load - pos_bc_value * pybamm.Vector(pos_bc_load)
+            boundary_load = boundary_load + pos_bc_value * pybamm.Vector(pos_bc_load)
         else:
             raise ValueError(
                 "boundary condition must be Dirichlet or Neumann, not '{}'".format(

sign error in fem dirichlet bcs
In FEM dirichlet BCs have the wrong sign 
diff --git a/tests/unit/test_processed_variable.py b/tests/unit/test_processed_variable.py
index a891fdbc6..87c29a84a 100644
--- a/tests/unit/test_processed_variable.py
+++ b/tests/unit/test_processed_variable.py
@@ -140,13 +140,11 @@ class TestProcessedVariable(unittest.TestCase):
 
     def test_processed_variable_3D_scikit(self):
         var = pybamm.Variable("var", domain=["current collector"])
-        y = pybamm.SpatialVariable("y", domain=["current collector"])
-        z = pybamm.SpatialVariable("z", domain=["current collector"])
 
         disc = tests.get_2p1d_discretisation_for_testing()
         disc.set_variable_slices([var])
-        y_sol = disc.process_symbol(y).entries[:, 0]
-        z_sol = disc.process_symbol(z).entries[:, 0]
+        y = disc.mesh["current collector"][0].edges["y"]
+        z = disc.mesh["current collector"][0].edges["z"]
         var_sol = disc.process_symbol(var)
         t_sol = np.linspace(0, 1)
         u_sol = np.ones(var_sol.shape[0])[:, np.newaxis] * np.linspace(0, 5)
@@ -154,25 +152,23 @@ class TestProcessedVariable(unittest.TestCase):
         processed_var = pybamm.ProcessedVariable(var_sol, t_sol, u_sol, mesh=disc.mesh)
         np.testing.assert_array_equal(
             processed_var.entries,
-            np.reshape(u_sol, [len(y_sol), len(z_sol), len(t_sol)]),
+            np.reshape(u_sol, [len(y), len(z), len(t_sol)]),
         )
 
     def test_processed_variable_2Dspace_scikit(self):
         var = pybamm.Variable("var", domain=["current collector"])
-        y = pybamm.SpatialVariable("y", domain=["current collector"])
-        z = pybamm.SpatialVariable("z", domain=["current collector"])
 
         disc = tests.get_2p1d_discretisation_for_testing()
         disc.set_variable_slices([var])
-        y_sol = disc.process_symbol(y).entries[:, 0]
-        z_sol = disc.process_symbol(z).entries[:, 0]
+        y = disc.mesh["current collector"][0].edges["y"]
+        z = disc.mesh["current collector"][0].edges["z"]
         var_sol = disc.process_symbol(var)
         t_sol = np.array([0])
         u_sol = np.ones(var_sol.shape[0])[:, np.newaxis]
 
         processed_var = pybamm.ProcessedVariable(var_sol, t_sol, u_sol, mesh=disc.mesh)
         np.testing.assert_array_equal(
-            processed_var.entries, np.reshape(u_sol, [len(y_sol), len(z_sol)])
+            processed_var.entries, np.reshape(u_sol, [len(y), len(z)])
         )
 
     def test_processed_var_1D_interpolation(self):
@@ -367,13 +363,11 @@ class TestProcessedVariable(unittest.TestCase):
 
     def test_processed_var_3D_scikit_interpolation(self):
         var = pybamm.Variable("var", domain=["current collector"])
-        y = pybamm.SpatialVariable("y", domain=["current collector"])
-        z = pybamm.SpatialVariable("z", domain=["current collector"])
 
         disc = tests.get_2p1d_discretisation_for_testing()
         disc.set_variable_slices([var])
-        y_sol = disc.process_symbol(y).entries[:, 0]
-        z_sol = disc.process_symbol(z).entries[:, 0]
+        y_sol = disc.mesh["current collector"][0].edges["y"]
+        z_sol = disc.mesh["current collector"][0].edges["z"]
         var_sol = disc.process_symbol(var)
         t_sol = np.linspace(0, 1)
         u_sol = np.ones(var_sol.shape[0])[:, np.newaxis] * np.linspace(0, 5)
@@ -406,13 +400,11 @@ class TestProcessedVariable(unittest.TestCase):
 
     def test_processed_var_2Dspace_scikit_interpolation(self):
         var = pybamm.Variable("var", domain=["current collector"])
-        y = pybamm.SpatialVariable("y", domain=["current collector"])
-        z = pybamm.SpatialVariable("z", domain=["current collector"])
 
         disc = tests.get_2p1d_discretisation_for_testing()
         disc.set_variable_slices([var])
-        y_sol = disc.process_symbol(y).entries[:, 0]
-        z_sol = disc.process_symbol(z).entries[:, 0]
+        y_sol = disc.mesh["current collector"][0].edges["y"]
+        z_sol = disc.mesh["current collector"][0].edges["z"]
         var_sol = disc.process_symbol(var)
         t_sol = np.array([0])
         u_sol = np.ones(var_sol.shape[0])[:, np.newaxis]
diff --git a/tests/unit/test_spatial_methods/test_scikit_finite_element.py b/tests/unit/test_spatial_methods/test_scikit_finite_element.py
index 5a108e275..21bd4b879 100644
--- a/tests/unit/test_spatial_methods/test_scikit_finite_element.py
+++ b/tests/unit/test_spatial_methods/test_scikit_finite_element.py
@@ -461,6 +461,68 @@ class TestScikitFiniteElement(unittest.TestCase):
         u_exact = z ** 2 / 2 - 1 / 6
         np.testing.assert_array_almost_equal(solution.y[:-1], u_exact, decimal=1)
 
+    def test_dirichlet_bcs(self):
+        # manufactured solution u = a*z^2 + b*z + c
+        model = pybamm.BaseModel()
+        a = 3
+        b = 4
+        c = 5
+        u = pybamm.Variable("variable", domain="current collector")
+        model.algebraic = {u: -pybamm.laplacian(u) + pybamm.source(2 * a, u)}
+        # set boundary conditions ("negative tab" = bottom of unit square,
+        # "positive tab" = top of unit square, elsewhere normal derivative is zero)
+        model.boundary_conditions = {
+            u: {
+                "negative tab": (pybamm.Scalar(c), "Dirichlet"),
+                "positive tab": (pybamm.Scalar(a + b + c), "Dirichlet"),
+            }
+        }
+        # bad initial guess (on purpose)
+        model.initial_conditions = {u: pybamm.Scalar(1)}
+        model.variables = {"u": u}
+        # create discretisation
+        mesh = get_unit_2p1D_mesh_for_testing(ypts=8, zpts=32)
+        spatial_methods = {
+            "macroscale": pybamm.FiniteVolume,
+            "current collector": pybamm.ScikitFiniteElement,
+        }
+        disc = pybamm.Discretisation(mesh, spatial_methods)
+        disc.process_model(model)
+
+        # solve model
+        solver = pybamm.AlgebraicSolver()
+        solution = solver.solve(model)
+
+        # indepedent of y, so just check values for one y
+        z = mesh["current collector"][0].edges["z"][:, np.newaxis]
+        u_exact = a * z ** 2 + b * z + c
+        np.testing.assert_array_almost_equal(solution.y[0 : len(z)], u_exact)
+
+    def test_disc_spatial_var(self):
+        mesh = get_unit_2p1D_mesh_for_testing(ypts=4, zpts=5)
+        spatial_methods = {
+            "macroscale": pybamm.FiniteVolume,
+            "current collector": pybamm.ScikitFiniteElement,
+        }
+        disc = pybamm.Discretisation(mesh, spatial_methods)
+
+        # discretise y and z
+        y = pybamm.SpatialVariable("y", ["current collector"])
+        z = pybamm.SpatialVariable("z", ["current collector"])
+        y_disc = disc.process_symbol(y)
+        z_disc = disc.process_symbol(z)
+
+        # create expected meshgrid
+        y_vec = np.linspace(0, 1, 4)
+        z_vec = np.linspace(0, 1, 5)
+        Y, Z = np.meshgrid(y_vec, z_vec)
+        y_actual = np.transpose(Y).flatten()[:, np.newaxis]
+        z_actual = np.transpose(Z).flatten()[:, np.newaxis]
+
+        # spatial vars should discretise to the flattend meshgrid
+        np.testing.assert_array_equal(y_disc.evaluate(), y_actual)
+        np.testing.assert_array_equal(z_disc.evaluate(), z_actual)
+
 
 if __name__ == "__main__":
     print("Add -v for more debug output")

pip install -e .[dev,docs]
parse_log_pytest
requirements.txt
pytest
apt-get update apt-get install -y gcc gfortran libopenblas-dev liblapack-dev
3.9
requirements/base.txt
pytest --no-header -rA --tb=line --color=no -p no:cacheprovider -W ignore::DeprecationWarning
alabaster==0.7.16
anyio==4.9.0
anytree==2.12.1
argon2-cffi==23.1.0
argon2-cffi-bindings==21.2.0
arrow==1.3.0
asttokens==3.0.0
async-lru==2.0.5
attrs==25.3.0
autograd==1.7.0
babel==2.17.0
beautifulsoup4==4.13.3
black==25.1.0
bleach==6.2.0
casadi==3.7.0
certifi==2025.1.31
cffi==1.17.1
charset-normalizer==3.4.1
click==8.1.8
comm==0.2.2
contourpy==1.3.0
cycler==0.12.1
debugpy==1.8.13
decorator==5.2.1
defusedxml==0.7.1
docutils==0.21.2
exceptiongroup==1.2.2
executing==2.2.0
fastjsonschema==2.21.1
flake8==7.2.0
fonttools==4.56.0
fqdn==1.5.1
guzzle_sphinx_theme==0.7.11
h11==0.14.0
httpcore==1.0.7
httpx==0.28.1
idna==3.10
imagesize==1.4.1
importlib_metadata==8.6.1
importlib_resources==6.5.2
iniconfig==2.1.0
ipykernel==6.29.5
ipython==8.18.1
ipywidgets==8.1.5
isoduration==20.11.0
jedi==0.19.2
Jinja2==3.1.6
json5==0.10.0
jsonpointer==3.0.0
jsonschema==4.23.0
jsonschema-specifications==2024.10.1
jupyter==1.1.1
jupyter-console==6.6.3
jupyter-events==0.12.0
jupyter-lsp==2.2.5
jupyter_client==8.6.3
jupyter_core==5.7.2
jupyter_server==2.15.0
jupyter_server_terminals==0.5.3
jupyterlab==4.3.6
jupyterlab_pygments==0.3.0
jupyterlab_server==2.27.3
jupyterlab_widgets==3.0.13
kiwisolver==1.4.7
MarkupSafe==3.0.2
matplotlib==3.9.4
matplotlib-inline==0.1.7
mccabe==0.7.0
mistune==3.1.3
mypy-extensions==1.0.0
nbclient==0.10.2
nbconvert==7.16.6
nbformat==5.10.4
nest-asyncio==1.6.0
notebook==7.3.3
notebook_shim==0.2.4
numpy==2.0.2
overrides==7.7.0
packaging==24.2
pandas==2.2.3
pandocfilters==1.5.1
parso==0.8.4
pathspec==0.12.1
pexpect==4.9.0
pillow==11.1.0
platformdirs==4.3.7
pluggy==1.5.0
prometheus_client==0.21.1
prompt_toolkit==3.0.50
psutil==7.0.0
ptyprocess==0.7.0
pure_eval==0.2.3
-e git+https://github.com/pybamm-team/PyBaMM.git@595a101ead908926283202a661c41ecd3508145a#egg=pybamm
pycodestyle==2.13.0
pycparser==2.22
pyflakes==3.3.1
Pygments==2.19.1
pyparsing==3.2.3
pytest==8.3.5
python-dateutil==2.9.0.post0
python-json-logger==3.3.0
pytz==2025.2
PyYAML==6.0.2
pyzmq==26.3.0
referencing==0.36.2
requests==2.32.3
rfc3339-validator==0.1.4
rfc3986-validator==0.1.1
rpds-py==0.24.0
scikit-fem==10.0.2
scipy==1.13.1
Send2Trash==1.8.3
six==1.17.0
sniffio==1.3.1
snowballstemmer==2.2.0
soupsieve==2.6
Sphinx==7.4.7
sphinxcontrib-applehelp==2.0.0
sphinxcontrib-devhelp==2.0.0
sphinxcontrib-htmlhelp==2.1.0
sphinxcontrib-jsmath==1.0.1
sphinxcontrib-qthelp==2.0.0
sphinxcontrib-serializinghtml==2.0.0
stack-data==0.6.3
terminado==0.18.1
tinycss2==1.4.0
tomli==2.2.1
tornado==6.4.2
traitlets==5.14.3
types-python-dateutil==2.9.0.20241206
typing_extensions==4.13.0
tzdata==2025.2
uri-template==1.3.0
urllib3==2.3.0
wcwidth==0.2.13
webcolors==24.11.1
webencodings==0.5.1
websocket-client==1.8.0
widgetsnbextension==4.0.13
zipp==3.21.0

name: PyBaMM
channels:
  - defaults
  - https://repo.anaconda.com/pkgs/main
  - https://repo.anaconda.com/pkgs/r
  - conda-forge
dependencies:
  - _libgcc_mutex=0.1=main
  - _openmp_mutex=5.1=1_gnu
  - ca-certificates=2025.2.25=h06a4308_0
  - ld_impl_linux-64=2.40=h12ee557_0
  - libffi=3.4.4=h6a678d5_1
  - libgcc-ng=11.2.0=h1234567_1
  - libgomp=11.2.0=h1234567_1
  - libstdcxx-ng=11.2.0=h1234567_1
  - ncurses=6.4=h6a678d5_0
  - openssl=3.0.16=h5eee18b_0
  - pip=25.0=py39h06a4308_0
  - python=3.9.21=he870216_1
  - readline=8.2=h5eee18b_0
  - setuptools=75.8.0=py39h06a4308_0
  - sqlite=3.45.3=h5eee18b_0
  - tk=8.6.14=h39e8969_0
  - wheel=0.45.1=py39h06a4308_0
  - xz=5.6.4=h5eee18b_1
  - zlib=1.2.13=h5eee18b_1
  - pip:
      - alabaster==0.7.16
      - anyio==4.9.0
      - anytree==2.12.1
      - argon2-cffi==23.1.0
      - argon2-cffi-bindings==21.2.0
      - arrow==1.3.0
      - asttokens==3.0.0
      - async-lru==2.0.5
      - attrs==25.3.0
      - autograd==1.7.0
      - babel==2.17.0
      - beautifulsoup4==4.13.3
      - black==25.1.0
      - bleach==6.2.0
      - casadi==3.7.0
      - certifi==2025.1.31
      - cffi==1.17.1
      - charset-normalizer==3.4.1
      - click==8.1.8
      - comm==0.2.2
      - contourpy==1.3.0
      - cycler==0.12.1
      - debugpy==1.8.13
      - decorator==5.2.1
      - defusedxml==0.7.1
      - docutils==0.21.2
      - exceptiongroup==1.2.2
      - executing==2.2.0
      - fastjsonschema==2.21.1
      - flake8==7.2.0
      - fonttools==4.56.0
      - fqdn==1.5.1
      - guzzle-sphinx-theme==0.7.11
      - h11==0.14.0
      - httpcore==1.0.7
      - httpx==0.28.1
      - idna==3.10
      - imagesize==1.4.1
      - importlib-metadata==8.6.1
      - importlib-resources==6.5.2
      - iniconfig==2.1.0
      - ipykernel==6.29.5
      - ipython==8.18.1
      - ipywidgets==8.1.5
      - isoduration==20.11.0
      - jedi==0.19.2
      - jinja2==3.1.6
      - json5==0.10.0
      - jsonpointer==3.0.0
      - jsonschema==4.23.0
      - jsonschema-specifications==2024.10.1
      - jupyter==1.1.1
      - jupyter-client==8.6.3
      - jupyter-console==6.6.3
      - jupyter-core==5.7.2
      - jupyter-events==0.12.0
      - jupyter-lsp==2.2.5
      - jupyter-server==2.15.0
      - jupyter-server-terminals==0.5.3
      - jupyterlab==4.3.6
      - jupyterlab-pygments==0.3.0
      - jupyterlab-server==2.27.3
      - jupyterlab-widgets==3.0.13
      - kiwisolver==1.4.7
      - markupsafe==3.0.2
      - matplotlib==3.9.4
      - matplotlib-inline==0.1.7
      - mccabe==0.7.0
      - mistune==3.1.3
      - mypy-extensions==1.0.0
      - nbclient==0.10.2
      - nbconvert==7.16.6
      - nbformat==5.10.4
      - nest-asyncio==1.6.0
      - notebook==7.3.3
      - notebook-shim==0.2.4
      - numpy==2.0.2
      - overrides==7.7.0
      - packaging==24.2
      - pandas==2.2.3
      - pandocfilters==1.5.1
      - parso==0.8.4
      - pathspec==0.12.1
      - pexpect==4.9.0
      - pillow==11.1.0
      - platformdirs==4.3.7
      - pluggy==1.5.0
      - prometheus-client==0.21.1
      - prompt-toolkit==3.0.50
      - psutil==7.0.0
      - ptyprocess==0.7.0
      - pure-eval==0.2.3
      - pycodestyle==2.13.0
      - pycparser==2.22
      - pyflakes==3.3.1
      - pygments==2.19.1
      - pyparsing==3.2.3
      - pytest==8.3.5
      - python-dateutil==2.9.0.post0
      - python-json-logger==3.3.0
      - pytz==2025.2
      - pyyaml==6.0.2
      - pyzmq==26.3.0
      - referencing==0.36.2
      - requests==2.32.3
      - rfc3339-validator==0.1.4
      - rfc3986-validator==0.1.1
      - rpds-py==0.24.0
      - scikit-fem==10.0.2
      - scipy==1.13.1
      - send2trash==1.8.3
      - six==1.17.0
      - sniffio==1.3.1
      - snowballstemmer==2.2.0
      - soupsieve==2.6
      - sphinx==7.4.7
      - sphinxcontrib-applehelp==2.0.0
      - sphinxcontrib-devhelp==2.0.0
      - sphinxcontrib-htmlhelp==2.1.0
      - sphinxcontrib-jsmath==1.0.1
      - sphinxcontrib-qthelp==2.0.0
      - sphinxcontrib-serializinghtml==2.0.0
      - stack-data==0.6.3
      - terminado==0.18.1
      - tinycss2==1.4.0
      - tomli==2.2.1
      - tornado==6.4.2
      - traitlets==5.14.3
      - types-python-dateutil==2.9.0.20241206
      - typing-extensions==4.13.0
      - tzdata==2025.2
      - uri-template==1.3.0
      - urllib3==2.3.0
      - wcwidth==0.2.13
      - webcolors==24.11.1
      - webencodings==0.5.1
      - websocket-client==1.8.0
      - widgetsnbextension==4.0.13
      - zipp==3.21.0
prefix: /opt/conda/envs/PyBaMM

tests/unit/test_spatial_methods/test_scikit_finite_element.py::TestScikitFiniteElement::test_disc_spatial_var
tests/unit/test_spatial_methods/test_scikit_finite_element.py::TestScikitFiniteElement::test_boundary_integral tests/unit/test_spatial_methods/test_scikit_finite_element.py::TestScikitFiniteElement::test_definite_integral tests/unit/test_spatial_methods/test_scikit_finite_element.py::TestScikitFiniteElement::test_definite_integral_vector tests/unit/test_spatial_methods/test_scikit_finite_element.py::TestScikitFiniteElement::test_dirichlet_bcs tests/unit/test_spatial_methods/test_scikit_finite_element.py::TestScikitFiniteElement::test_discretise_equations tests/unit/test_spatial_methods/test_scikit_finite_element.py::TestScikitFiniteElement::test_manufactured_solution tests/unit/test_spatial_methods/test_scikit_finite_element.py::TestScikitFiniteElement::test_manufactured_solution_cheb_grid tests/unit/test_spatial_methods/test_scikit_finite_element.py::TestScikitFiniteElement::test_manufactured_solution_exponential_grid tests/unit/test_spatial_methods/test_scikit_finite_element.py::TestScikitFiniteElement::test_neg_pos tests/unit/test_spatial_methods/test_scikit_finite_element.py::TestScikitFiniteElement::test_pure_neumann_poisson
tests/unit/test_processed_variable.py::TestProcessedVariable::test_call_failure tests/unit/test_processed_variable.py::TestProcessedVariable::test_processed_var_1D_interpolation tests/unit/test_processed_variable.py::TestProcessedVariable::test_processed_var_2D_interpolation tests/unit/test_processed_variable.py::TestProcessedVariable::test_processed_var_2Dspace_scikit_interpolation tests/unit/test_processed_variable.py::TestProcessedVariable::test_processed_var_3D_interpolation tests/unit/test_processed_variable.py::TestProcessedVariable::test_processed_var_3D_r_first_dimension tests/unit/test_processed_variable.py::TestProcessedVariable::test_processed_var_3D_scikit_interpolation tests/unit/test_processed_variable.py::TestProcessedVariable::test_processed_variable_1D tests/unit/test_processed_variable.py::TestProcessedVariable::test_processed_variable_2D tests/unit/test_processed_variable.py::TestProcessedVariable::test_processed_variable_2D_unknown_domain tests/unit/test_processed_variable.py::TestProcessedVariable::test_processed_variable_2Dspace_scikit tests/unit/test_processed_variable.py::TestProcessedVariable::test_processed_variable_3D_scikit tests/unit/test_processed_variable.py::TestProcessedVariable::test_processed_variable_3D_x_r tests/unit/test_processed_variable.py::TestProcessedVariable::test_processed_variable_3D_x_z tests/unit/test_processed_variable.py::TestProcessedVariable::test_processed_variable_ode_pde_solution tests/unit/test_spatial_methods/test_scikit_finite_element.py::TestScikitFiniteElement::test_not_implemented
pybamm/spatial_methods/scikit_finite_element.py CHANGELOG.md
pybamm/spatial_methods/scikit_finite_element.py CHANGELOG.md