diff --git a/firedrake/assemble.py b/firedrake/assemble.py
index afd7076114..a1d0009eb1 100644
--- a/firedrake/assemble.py
+++ b/firedrake/assemble.py
@@ -385,6 +385,12 @@ def visitor(e, *operands):
         visited = {}
         result = BaseFormAssembler.base_form_postorder_traversal(self._form, visitor, visited)
 
+        # Apply BCs after assembly
+        rank = len(self._form.arguments())
+        if rank == 1:
+            for bc in self._bcs:
+                bc.zero(result)
+
         if tensor:
             BaseFormAssembler.update_tensor(result, tensor)
             return tensor
@@ -409,7 +415,7 @@ def base_form_assembly_visitor(self, expr, tensor, *args):
             if rank == 0:
                 assembler = ZeroFormAssembler(form, form_compiler_parameters=self._form_compiler_params)
             elif rank == 1 or (rank == 2 and self._diagonal):
-                assembler = OneFormAssembler(form, bcs=self._bcs, form_compiler_parameters=self._form_compiler_params,
+                assembler = OneFormAssembler(form, form_compiler_parameters=self._form_compiler_params,
                                              zero_bc_nodes=self._zero_bc_nodes, diagonal=self._diagonal, weight=self._weight)
             elif rank == 2:
                 assembler = TwoFormAssembler(form, bcs=self._bcs, form_compiler_parameters=self._form_compiler_params,
@@ -811,9 +817,9 @@ def restructure_base_form(expr, visited=None):
             return ufl.action(expr, ustar)
 
         # -- Case (6) -- #
-        if isinstance(expr, ufl.FormSum) and all(isinstance(c, ufl.core.base_form_operator.BaseFormOperator) for c in expr.components()):
+        if isinstance(expr, ufl.FormSum) and all(not isinstance(c, ufl.form.BaseForm) for c in expr.components()):
             # Return ufl.Sum
-            return sum([c for c in expr.components()])
+            return sum(w*c for w, c in zip(expr.weights(), expr.components()))
         return expr
 
     @staticmethod
diff --git a/firedrake/variational_solver.py b/firedrake/variational_solver.py
index 488b42d55c..3c8fc8b930 100644
--- a/firedrake/variational_solver.py
+++ b/firedrake/variational_solver.py
@@ -9,11 +9,12 @@
     PETSc, OptionsManager, flatten_parameters, DEFAULT_KSP_PARAMETERS,
     DEFAULT_SNES_PARAMETERS
 )
-from firedrake.function import Function, Cofunction
-from firedrake.ufl_expr import TrialFunction, TestFunction
+from firedrake.function import Function
+from firedrake.ufl_expr import TrialFunction, TestFunction, action
 from firedrake.bcs import DirichletBC, EquationBC, extract_subdomain_ids, restricted_function_space
 from firedrake.adjoint_utils import NonlinearVariationalProblemMixin, NonlinearVariationalSolverMixin
-from ufl import replace
+from firedrake.__future__ import interpolate
+from ufl import replace, Form
 
 __all__ = ["LinearVariationalProblem",
            "LinearVariationalSolver",
@@ -91,12 +92,11 @@ def __init__(self, F, u, bcs=None, J=None,
             bcs = [bc.reconstruct(V=V_res, indices=bc._indices) for bc in bcs]
             self.u_restrict = Function(V_res).interpolate(u)
             v_res, u_res = TestFunction(V_res), TrialFunction(V_res)
-            F_arg, = F.arguments()
-            replace_F = {F_arg: v_res, self.u: self.u_restrict}
-            for c in F.coefficients():
-                if c.function_space() == V.dual():
-                    replace_F[c] = Cofunction(V_res.dual()).interpolate(c)
-            self.F = replace(F, replace_F)
+            if isinstance(F, Form):
+                F_arg, = F.arguments()
+                self.F = replace(F, {F_arg: v_res, self.u: self.u_restrict})
+            else:
+                self.F = action(replace(F, {self.u: self.u_restrict}), interpolate(v_res, V))
             v_arg, u_arg = self.J.arguments()
             self.J = replace(self.J, {v_arg: v_res, u_arg: u_res, self.u: self.u_restrict})
             if self.Jp: