Efficient analytical integration of symmetric Galerkin boundary integrals over curved elements: Thermal conduction formulation

A posteriori pointwise error estimates for the boundary element method

“…Table 2 compares the results obtained with the present implementation and those reported in Reference [5] for the symmetric Galerkin boundary element analysis with analytical evaluation of singular integrals. The discretization used in Reference [5] consists of 92 distinct nodes and 46 isoparametric quadratic elements. The present discretization and the one in Reference [5] have the same set of nodal points in the boundary element mesh.…”

“…The last example, extracted from Reference [5], is reasonably representative of geometry and boundary conditions that arise in practice, and it does not have an analytical solution. The geometry is shown in Figure 17.…”

“…The discretization used in Reference [5] consists of 92 distinct nodes and 46 isoparametric quadratic elements. The present discretization and the one in Reference [5] have the same set of nodal points in the boundary element mesh. From Table 2, it is observed that a good agreement between the two boundary element solutions is achieved.…”

Analytical integrations in 2D BEM elasticity

“…The relative error along the circumference of radius a is expressed by means of the variable as in Equation (39). The absolute error along the circumference of radius b is expressed by means of the variable := log 10 |ˆ r (x)| (40) for being r (x) = 0 (see Equation (38)). Remarks made for the h-technique on the displacement ÿeld applies also to the stress ÿeld.…”

“…There is nowadays an extensive literature on this subject (see, among others [38][39][40][41][42][43][44]). A huge amount of literature concerns the numerical evaluation of hypersingular integrals: among others [15; 18; 19; 38; 45-47].…”