Electrocardiographic imaging (ECGI) facilitates the non-invasive reconstruction of electrical activity in the entire heart at once. ECGI requires both recordings of multi-channel ECG signals as well as an MRI-based model of the thorax. The model is used to solve the underlying Poissons problem, which relates the gradient of transmembrane voltages in the heart to the ECG and is a spatial differential equation. In ECGI, this relationship has to be established before starting inverse calculations, i.e. the forward problem has to be solved. It solution depends strongly on the spatial discretization of the model, as its resolution affects the representation of the source gradients. To study the convergence of resolution-related effects in the forward problem, we use a simplified thorax model which allows for very high resolutions. An ECG is produced for the excitation origin of a premature ventricular contraction in the apex. The study reveals that the greatest resolution-related effects vanish below a resolution of 5 mm of the cardiac tissue. At below 1 mm, resolution effects stabilize and only marginal effects from the spatial structure of the mesh persist down to a resolution of 0.25 mm.