This paper sets out a three-dimensional (3D) boundary element method (BEM) formulation in the frequency domain to simulate heat transfer through a point thermal bridge (PTB) at a corner in a building envelope. The main purpose was to quantify the dynamic effect of a geometrical PTB in terms of distribution of temperatures and heat fluxes, which is useful for evaluating moisture condensation risk. The numerical model is first validated experimentally using a hot box to measure the dynamic heat behavior of a 3D timber building corner. The proposed model is then used to study the dynamic thermal bridging effect in the vicinity of a 3D concrete corner. Given the importance of the risk of condensation, this study looks at the influence of an insulating material and its position on the temperature and heat flux distribution through the PTB under steady state and dynamic conditions.

The evaluation of the singular and hypersingular integrals that appear in three‐dimensional boundary element formulations for heat diffusion, in the frequency domain, is presented in analytical form. This improves computational efficiency and accuracy. Numerical integrations using existing techniques based on standard Gaussian integration schemes that incorporate an enormous amount of sampling points are used to verify the solutions of singular integrals. For the hypersingular integrals the comparison is evaluated by making use of an analytical solution that is valid for circular domains, combined with a standard Gaussian integration scheme for the remaining boundary element domain. Closed form solutions for cylindrical inclusions (with null temperatures and null heat fluxes prescribed on the boundary) are then derived and used to validate the three‐dimensional boundary element formulations.