* But it requires the continuity just in integral sense:
* any function in the space should have the same integral values on two sides of the common edge shared by two adjacent elements.
- * Thus each function in the nonconforming element space can be discontinuous, not included in H^1_0, as functions in Discontinuous Galerkin (DG) finite element spaces.
+ * Thus each function in the nonconforming element space can be discontinuous, not included in H^1_0, as functions in Discontinuous Galerkin (DG) finite element spaces.
* Although any function in DG element space also has nonconformity, it is completely discontinuous across edges without any relation.
* It is a reason why usual weak formulations for DG schemes contain additional penalty terms for jump across edges to control discontinuity.
* However nonconforming elements usually do not need additional terms in their weak formulations due to the continuity in integral on edges.
* </ul>
* Note that above shape functions are constructed on each cell, not on the reference cell only.
- * @p get_linear_shape computes the coefficients for shape functions when @p fill_fe_values is called on each cell.
+ * @p get_linear_shape computes the coefficients for shape functions when @p fill_fe_values is called on each cell.
* The (global) basis function associated with a node is defined by the composition of
* (local) basis functions associated with the node on each element.
* Contrast with ordinary Lagrange finite elements, DOF value with respect to the P1 nonconforming element at given node does not coincide with the function value at that node.
* For instance, the (global) basis function associated with a node has 0.75 at that node, not 1.0.
* Thus we need an interpolation operator which maps any smooth function into a function with proper DOF values in the P1 element space.
- * One natural interpolant associated with given smooth function is the linear function whose midpoint value at each edge is defined by
+ * One natural interpolant associated with given smooth function is the linear function whose midpoint value at each edge is defined by
* the average of two values at endpoints of the edge.
* It provides appropriate weights used in @p unit_support_points.