2013/12/09 by Lorenz Berger, Berger, Lorenz, Rafel Bordas +5 · 2 citations
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Elasticity and Material Modeling #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1312.2607
openalex publication_date 2013/12/09 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28
A stabilized conforming mixed finite element method for the three-field\n(displacement, fluid flux and pressure) poroelasticity problem is developed and\nanalyzed. We use the lowest possible approximation order, namely piecewise\nconstant approximation for the pressure and piecewise linear continuous\nelements for the displacements and fluid flux. By applying a local pressure\njump stabilization term to the mass conservation equation we ensure stability\nand avoid pressure oscillations. Importantly, the discretization leads to a\nsymmetric linear system. For the fully discretized problem we prove existence\nand uniqueness, an energy estimate and an optimal a-priori error estimate,\nincluding an error estimate for the divergence of the fluid flux. Numerical\nexperiments in 2D and 3D illustrate the convergence of the method, show the\neffectiveness of the method to overcome spurious pressure oscillations, and\nevaluate the added mass effect of the stabilization term.\n