Enriched and Discontinuous Galerkin Discretizations for a Cardiac Mechanics Benchmark Problem

Computer models of the human heart enhance understanding of cardiac function but require a compromise between computational cost and numerical accuracy for clinical use.Due to the high mathematical complexity of the underlying model, the commonly used finite element discretization may not achieve the optimal balance between efficiency, reliability, and accuracy.To investigate the impact of different spatial discretization schemes on cardiac mechanics, we realized a benchmark configuration, which considers the hyper-elastic problem of inflating and actively contracting an idealized left ventricle with transversely isotropic and nearly incompressible properties.Comparing linear and quadratic conforming Galerkin, discontinuous Galerkin and enriched Galerkin elements, we found that enriched and discontinuous Galerkin methods reduced locking phenomena but with higher numbers of degrees of freedom and computational costs, particularly for the discontinuous Galerkin approach.However, enriched Galerkin demonstrated comparable robustness to discontinuous Galerkin with substantially fewer degrees of freedom, presenting a favorable compromise between computational efficiency and numerical robustness.