diff --git a/pySDC/implementations/problem_classes/AdvectionDiffusionEquation_1D_FFT.py b/pySDC/implementations/problem_classes/AdvectionDiffusionEquation_1D_FFT.py
index 8e164ed88f..beb56d3c79 100644
--- a/pySDC/implementations/problem_classes/AdvectionDiffusionEquation_1D_FFT.py
+++ b/pySDC/implementations/problem_classes/AdvectionDiffusionEquation_1D_FFT.py
@@ -1,7 +1,7 @@
 import numpy as np
 
 from pySDC.core.Errors import ParameterError, ProblemError
-from pySDC.core.Problem import ptype
+from pySDC.core.Problem import ptype, WorkCounter
 from pySDC.implementations.datatype_classes.mesh import mesh, imex_mesh
 
 
@@ -70,6 +70,8 @@ def __init__(self, nvars=256, c=1.0, freq=-1, nu=0.02, L=1.0):
         self.ddx = kx * 1j
         self.lap = -(kx**2)
 
+        self.work_counters['rhs'] = WorkCounter()
+
     def eval_f(self, u, t):
         """
         Routine to evaluate the right-hand side of the problem.
@@ -94,6 +96,7 @@ def eval_f(self, u, t):
         f.impl[:] = np.fft.irfft(tmp_impl)
         f.expl[:] = np.fft.irfft(tmp_expl)
 
+        self.work_counters['rhs']()
         return f
 
     def solve_system(self, rhs, factor, u0, t):
@@ -153,6 +156,8 @@ def u_exact(self, t):
                     for i in range(self.init[0]):
                         x = self.xvalues[i] - self.c * t + k * self.L
                         me[i] += np.sqrt(t00) / np.sqrt(t00 + t) * np.exp(-(x**2) / (4.0 * self.nu * (t00 + t)))
+            else:
+                raise ParameterError("There is no exact solution implemented for negative frequency and negative nu!")
         return me
 
 
@@ -177,6 +182,9 @@ class advectiondiffusion1d_implicit(advectiondiffusion1d_imex):
     This class has the same attributes as the class it inherits from.
     """
 
+    dtype_u = mesh
+    dtype_f = mesh
+
     def eval_f(self, u, t):
         """
         Routine to evaluate the right-hand side of the problem.
@@ -199,6 +207,7 @@ def eval_f(self, u, t):
         tmp = self.nu * self.lap * tmp_u - self.c * self.ddx * tmp_u
         f[:] = np.fft.irfft(tmp)
 
+        self.work_counters['rhs']
         return f
 
     def solve_system(self, rhs, factor, u0, t):
diff --git a/pySDC/tests/test_problems/test_AdvectionDiffusionEquation_1D_FFT.py b/pySDC/tests/test_problems/test_AdvectionDiffusionEquation_1D_FFT.py
new file mode 100644
index 0000000000..0f5736f143
--- /dev/null
+++ b/pySDC/tests/test_problems/test_AdvectionDiffusionEquation_1D_FFT.py
@@ -0,0 +1,94 @@
+import pytest
+
+
+@pytest.mark.base
+@pytest.mark.parametrize('freq', [-1, 0, 1])
+@pytest.mark.parametrize('nu', [0.02, -0.02])
+def test_imex_vs_implicit(freq, nu):
+    import numpy as np
+    from pySDC.core.Errors import ParameterError, ProblemError
+    from pySDC.implementations.problem_classes.AdvectionDiffusionEquation_1D_FFT import (
+        advectiondiffusion1d_imex,
+        advectiondiffusion1d_implicit,
+    )
+
+    problem_params = {
+        'nvars': 32,
+        'c': 1.0,
+        'freq': freq,
+        'nu': nu,
+        'L': 1.0,
+    }
+
+    imex = advectiondiffusion1d_imex(**problem_params)
+    fully_impl = advectiondiffusion1d_implicit(**problem_params)
+
+    t0 = 0.0
+    if freq < 0 and nu < 0:
+        # check if ParameterError is raised correctly for freq < 0 and nu < 0
+        with pytest.raises(ParameterError):
+            imex.u_exact(t0)
+    else:
+        # test if evaluations of right-hand side do match
+        u0 = imex.u_exact(t0)
+
+        tmp = imex.eval_f(u0, t0)
+        f_imex = tmp.expl + tmp.impl
+        f_full = fully_impl.eval_f(u0, t0)
+
+        assert np.allclose(
+            f_imex, f_full
+        ), 'Evaluation of right-hand side in semi-explicit case and in fully-implicit case do not match!'
+
+        # test if solving one time step satisfies a specific error threshold
+        dt = 1e-3
+        args = {
+            'rhs': u0,
+            'factor': dt,
+            'u0': u0,
+            't': t0,
+        }
+
+        u_ex = imex.u_exact(t0 + dt)
+
+        u_imex = imex.solve_system(**args)
+        u_full = fully_impl.solve_system(**args)
+
+        e_imex = abs(u_ex - u_imex)
+        e_full = abs(u_ex - u_full)
+
+        e_tol_imex = {
+            -1: {
+                0.02: 0.011,
+            },
+            0: {
+                -0.02: 0.076,
+                0.02: 0.055,
+            },
+            1: {
+                -0.02: 0.0063,
+                0.02: 0.0063,
+            },
+        }
+
+        e_tol_full = {
+            -1: {
+                0.02: 0.00021,
+            },
+            0: {
+                -0.02: 0.078,
+                0.02: 0.064,
+            },
+            1: {
+                -0.02: 2.01e-05,
+                0.02: 2e-05,
+            },
+        }
+        assert e_imex < e_tol_imex[freq][nu], "Error is too large in semi-explicit case!"
+        assert e_full < e_tol_full[freq][nu], "Error is too large in fully-implicit case!"
+
+        # check if ProblemError is raised correctly in case if nvars % 2 != 0
+        problem_params.update({'nvars': 31})
+        with pytest.raises(ProblemError):
+            imex_test = advectiondiffusion1d_imex(**problem_params)
+            fully_impl_test = advectiondiffusion1d_implicit(**problem_params)