## 1 Introduction  
Microwaves are a form of electromagnetic radiation with wave frequencies (wavelengths) ranging from 300 MHz (\(\lambda\) = 1 m) up to 300 GHz (\(\lambda\) = 1 mm) [1]. Microwave technology is nowadays present in numerous fields and is utilized in the radar and communication industry [2], in laboratory measurements [3], in medical and scientific appliances [4], and in the field of chemistry [5]. This article focuses on issues related to the use of microwaves as an alternative method for heating and drying. Microwaves in this case are converted into heat by interacting with dielectric dipolar materials.  
The most common substance that can easily absorb microwave energy and can dissipate it as heat is water [6] as it is presented in Figure 1. Additionally, some carbon-based materials react like dielectric materials, as they contain freely moving delocalized \(\pi\)-electrons [7, 8, 9, 10].  
In general, microwaves enable selective heating, rapid and high efficiency heat transfer, and device miniaturization, while decreasing the cost of energy used and environment pollution [12].  
Microwave heating is widely used in the areas of material science [13; 14], analytical chemistry [15], food processing [16; 17], processing of materials [18], metal fractionation in sewage sludge [19], organic synthesis [20], polymer synthesis [21; 22], hospital waste sterilization [23], and wood drying [24].  
Microwave heaters are excited through the use of a magnetron that produces fixed frequency oscillations. The microwaves are then guided to a microwave resonance chamber, where standing waves occur, increasing wave amplitude. Alternatively, microwaves can be applied to non-resonant cavities; in this case, high RF energy absorption occurs where no standing wave is generated. In both cases, however, the delivered energy is generated in the magnetron.  
Designing a device especially equipped with a resonant chamber requires complex calculations based on field theory [25]. Building and testing prototypes is time consuming and highly ineffective. An alternative to physical models is computational modelling, which uses the finite element method for solving differential equations describing a specific physical phenomenon [26; 27].  
A key factor in accurate FEM calculations is mesh density [28; 29; 30]. Although Elmer FEM enables the use of second-order elements, the microwave ElmerSolver works only on tetrahedrons, so the shape of the elements used in the experiment is not discussed. The size of the involved elements has a great influence on the quality of the model. Small tetrahedral elements allow for more reliable solid representation and more accurate results. However, they are affected by a radical increase in calculation cost and memory resources. Moreover, this causes an unacceptably long time to be required to reach convergence on a solution. Furthermore, increasing mesh granularity makes the simulation more sensitive to numerical errors, such that it requires the more precise parameters of reality, which are sometimes difficult to get. Therefore, a compromise between mesh granularity, which is directly connected with calculation accuracy, and time consumption must be found.  
The aim of this paper is to examine the influence of mesh granularity on the accuracy of FEM modelling of the resonant state in a microwave resonant chamber. The most commonly used chambers are rectangular and cylindrical chambers. The chamber could have any shape, but rectangular and cylindrical are most frequently used; hence, the authors decided to model a cylindrical chamber. The modelling was carried out utilizing ELMER FEM open-source software enabling FEM-based modelling of microwave resonant states [31; 32]. The following section provides a detailed description of the chamber's geometric design process.