diff --git a/modules/electromagnetics/include/kernels/DivField.h b/modules/electromagnetics/include/kernels/DivField.h
new file mode 100644
index 000000000000..465d99795637
--- /dev/null
+++ b/modules/electromagnetics/include/kernels/DivField.h
@@ -0,0 +1,37 @@
+//* This file is part of the MOOSE framework
+//* https://www.mooseframework.org
+//*
+//* All rights reserved, see COPYRIGHT for full restrictions
+//* https://github.com/idaholab/moose/blob/master/COPYRIGHT
+//*
+//* Licensed under LGPL 2.1, please see LICENSE for details
+//* https://www.gnu.org/licenses/lgpl-2.1.html
+
+#pragma once
+
+#include "Kernel.h"
+
+/**
+ *  Weak form contribution corresponding to div(u) where u is a vector
+ */
+class DivField : public Kernel
+{
+public:
+  static InputParameters validParams();
+
+  DivField(const InputParameters & parameters);
+
+protected:
+  virtual Real computeQpResidual() override;
+  virtual Real computeQpOffDiagJacobian(unsigned jvar) override;
+
+  VectorMooseVariable & _u_var;
+
+  /// div of the shape function
+  const VectorVariablePhiDivergence & _div_phi;
+
+  /// holds the solution div at the current quadrature points
+  const VectorVariableDivergence & _div_u;
+
+  unsigned int _u_var_num;
+};
diff --git a/modules/electromagnetics/include/kernels/GradField.h b/modules/electromagnetics/include/kernels/GradField.h
new file mode 100644
index 000000000000..7d25a58121e9
--- /dev/null
+++ b/modules/electromagnetics/include/kernels/GradField.h
@@ -0,0 +1,39 @@
+//* This file is part of the MOOSE framework
+//* https://www.mooseframework.org
+//*
+//* All rights reserved, see COPYRIGHT for full restrictions
+//* https://github.com/idaholab/moose/blob/master/COPYRIGHT
+//*
+//* Licensed under LGPL 2.1, please see LICENSE for details
+//* https://www.gnu.org/licenses/lgpl-2.1.html
+
+#pragma once
+
+#include "VectorKernel.h"
+
+/**
+ *  Weak form contribution corresponding to -grad(p) where p is a scalar
+ */
+class GradField : public VectorKernel
+{
+public:
+  static InputParameters validParams();
+
+  GradField(const InputParameters & parameters);
+
+protected:
+  virtual Real computeQpResidual() override;
+  virtual Real computeQpOffDiagJacobian(unsigned jvar) override;
+
+  const VariableValue & _p;
+
+  MooseVariable & _p_var;
+
+  /// shape function
+  const VariablePhiValue & _p_phi;
+
+  /// div of the test function
+  const VectorVariableTestDivergence & _div_test;
+
+  unsigned int _p_var_num;
+};
diff --git a/modules/electromagnetics/src/kernels/DivField.C b/modules/electromagnetics/src/kernels/DivField.C
new file mode 100644
index 000000000000..293ccb51a013
--- /dev/null
+++ b/modules/electromagnetics/src/kernels/DivField.C
@@ -0,0 +1,46 @@
+//* This file is part of the MOOSE framework
+//* https://www.mooseframework.org
+//*
+//* All rights reserved, see COPYRIGHT for full restrictions
+//* https://github.com/idaholab/moose/blob/master/COPYRIGHT
+//*
+//* Licensed under LGPL 2.1, please see LICENSE for details
+//* https://www.gnu.org/licenses/lgpl-2.1.html
+
+#include "DivField.h"
+#include "Assembly.h"
+
+registerMooseObject("ElectromagneticsApp", DivField);
+
+InputParameters
+DivField::validParams()
+{
+  InputParameters params = Kernel::validParams();
+  params.addClassDescription("Weak form term for $\\nabla \\cdot \\vec{u}$.");
+  params.addRequiredCoupledVar("u", "vector field");
+  return params;
+}
+
+DivField::DivField(const InputParameters & parameters)
+  : Kernel(parameters),
+    _u_var(*getVectorVar("u", 0)),
+    _div_phi(_assembly.divPhi(_u_var)),
+    _div_u(_u_var.divSln()),
+    _u_var_num(coupled("u"))
+{
+}
+
+Real
+DivField::computeQpResidual()
+{
+  return _div_u[_qp] * _test[_i][_qp];
+}
+
+Real
+DivField::computeQpOffDiagJacobian(unsigned int jvar)
+{
+  if (_u_var_num == jvar)
+    return _div_phi[_j][_qp] * _test[_i][_qp];
+  
+  return 0.0;
+}
diff --git a/modules/electromagnetics/src/kernels/GradField.C b/modules/electromagnetics/src/kernels/GradField.C
new file mode 100644
index 000000000000..87c04a6bcb2a
--- /dev/null
+++ b/modules/electromagnetics/src/kernels/GradField.C
@@ -0,0 +1,47 @@
+//* This file is part of the MOOSE framework
+//* https://www.mooseframework.org
+//*
+//* All rights reserved, see COPYRIGHT for full restrictions
+//* https://github.com/idaholab/moose/blob/master/COPYRIGHT
+//*
+//* Licensed under LGPL 2.1, please see LICENSE for details
+//* https://www.gnu.org/licenses/lgpl-2.1.html
+
+#include "GradField.h"
+#include "Assembly.h"
+
+registerMooseObject("ElectromagneticsApp", GradField);
+
+InputParameters
+GradField::validParams()
+{
+  InputParameters params = VectorKernel::validParams();
+  params.addClassDescription("Weak form term for $-\\nabla p$.");
+  params.addRequiredCoupledVar("p", "scalar field");
+  return params;
+}
+
+GradField::GradField(const InputParameters & parameters)
+  : VectorKernel(parameters),
+    _p(coupledValue("p")),
+    _p_var(*getVar("p", 0)),
+    _p_phi(_assembly.phi(_p_var)),
+    _div_test(_var.divPhi()),
+    _p_var_num(coupled("p"))
+{
+}
+
+Real
+GradField::computeQpResidual()
+{
+  return _p[_qp] * _div_test[_i][_qp];
+}
+
+Real
+GradField::computeQpOffDiagJacobian(unsigned int jvar)
+{
+  if (_p_var_num == jvar) 
+    return _p_phi[_j][_qp] * _div_test[_i][_qp];
+  
+  return 0.0;
+}