Elements and boundaries for transient diffusion problems with infinite domains

•A new kind of one-dimensional infinite element is introduced.•A way to apply the new element as a boundary condition to the system is explained.•A two-dimensional transient boundary condition is presented.•Proposed techniques give better results than an existing infinite element analyzed.

The most common techniques in engineering to solve problems involving infinite domains employ infinite elements, together with conventional finite elements. This work analyzes the infinite element created by Zhao and Valliappan and proposes a new kind of infinite element, aiming to get better solutions in situations in which the former does not give satisfactory results. This new element is also applied alternatively as a boundary condition to the system, and then extended to two-dimensional problems. Examples are solved, verifying mesh refinement and time step influence in the results and comparing the techniques, giving better results to the proposed ones.