## 4 Conclusions  
There exist many different possibilities in the FEM community when choosing the shape of the finite element. For versatility and convenience, specific techniques are sometimes developed only for tetrahedra or hexahedra. To effectively choose the discretization shape in terms of the geometry of the problem, we need to develop the same techniques for all the shapes.  
Specifically, the use of adaptive techniques is very popular to save computational resources and introduce smart meshes where the areas that contribute more to the error are further refined. However, the use of these techniques applied to triangular prisms is not so common in the literature, whereas the use of these elements is quite advantageous in some scenarios (e.g., in planar circuits or thin material layers). For this reason, we have developed an adaptivity technique specifically designed for triangular prisms.  
We can summarize the main contributions of this paper with the following points:  
* We have introduced an estimator inspired by [34], with minor modifications to adjust the use of triangular prisms.
* We have experimented with five different marking strategies, modified to be adapted to the semi-structured nature of the triangular prism.
* We have suggested a refinement technique based on the _red-green_ algorithm from [43].
* We have introduced specific criteria to increase the quality of the generated meshes: specifically, we avoid the eyes in the mesh and the appearance of highly deformed triangles.
* We have developed a conformation process to avoid the problem of the hanging nodes.  
We have validated with numerical results the performance of the algorithm. We have shown the different behavior of each marking strategy: strategies based on the energy of the residual for each element show smaller elements around areas of stronger error, whereas strategies based on a given threshold of the element with maximum error yield more uniform meshes. In contrast, strategies based on refining a given percentage of the elements lead to more irregular meshes. All of the strategies provide smaller elements in higher error areas for both MMS and propagation problems. In addition, we have shown the performance of the algorithm with a singularity due to the geometry of the problem to be solved. This algorithm provides smaller elements in the vicinity of the singularity, as expected giving a better approximation of the singularity with fewer unknowns compared to the uniform refinement.  
As future research lines, the treatment of hanging nodes would eliminate the process of conformation, easing the step of refinement. Moreover, we could detect in which direction the estimator is more needed and apply the refinement only in the _horizontal_ or _vertical_ direction as detected.  
Figure 23: Representation of the singularity with different levels of \(h\) refinement.  
**Author Contributions:** Conceptualization, A.A.-M. and L.E.G.-C.; software, A.A.-M.; validation, A.A.-M. and L.E.G.-C.; investigation, A.A.-M. and L.E.G.-C.; data curation, A.A.-M.; writing--original draft preparation, A.A.-M.; writing--review and editing, L.E.G.-C.; supervision, L.E.G.-C.; resources, L.E.G.-C.; funding acquisition, L.E.G.-C. Both authors have read and agreed to the published version of the manuscript.  
**Funding:** This work has been financially supported by TEC2016-80386-P.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.  
**Conflicts of Interest:** The authors declare no conflict of interest.