Estimate of the effectiveness of the circular element in BEM and FEM

Utility and efficiency of a new circular element in BEM and FEM is outlined. The circular element is described with shape functions defined in polar coordinates and it is the base to define the circular model (MC)(MC). The model based on triangular elements (MT)(MT) which uses the same number of nodes is built for comparison. The efficiency of the circular element in FEM is examined by applying it to the modelling the circular membrane vibration problem. Next, this element is applied in BEM to the modelling the boundary in the simplest radiation acoustic problem. The advantage of the circular element is pointed out by examining two measures defined in this paper. Both measures compare, in some sense, the solutions of above-mentioned problems with the exact one. Consequently, the quality of MTMT is compared to the quality of MCMC indirectly. Numerical exercises confirm better quality of MCMC than MTMT.