• An accelerated staggered scheme for variational phase-field models of brittle fracture 

      Storvik, Erlend; Both, Jakub Wiktor; Sargado, Juan Michael Uy Villanueva; Nordbotten, Jan Martin; Radu, Florin Adrian (Journal article; Peer reviewed, 2021)
      There is currently an increasing interest in developing efficient solvers for variational phase-field models of brittle fracture. The governing equations for this problem originate from a constrained minimization of a ...
    • A Cahn-Hilliard-Biot system and its generalized gradient flow structure 

      Storvik, Erlend; Both, Jakub Wiktor; Nordbotten, Jan Martin; Radu, Adrian Florin (Journal article; Peer reviewed, 2022)
      In this work, we propose a new model for flow through deformable porous media, where the solid material has two phases with distinct material properties. The two phases of the porous material evolve according to a generalized ...
    • Global existence of weak solutions to unsaturated poroelasticity 

      Both, Jakub Wiktor; Pop, Iuliu Sorin; Yotov, Ivan (Journal article; Peer reviewed, 2021)
      We study unsaturated poroelasticity, i.e., coupled hydro-mechanical processes in variably saturated porous media, here modeled by a non-linear extension of Biot’s well-known quasi-static consolidation model. The coupled ...
    • Iterative splitting schemes for a soft material poromechanics model 

      Both, Jakub Wiktor; Barnafi, Nicolas; Radu, Florin Adrian; Zunino, Paolo; Quarteroni, Alfio (Journal article; Peer reviewed, 2021)
      We address numerical solvers for a poromechanics model particularly adapted for soft materials, as it generally respects thermodynamics principles and energy balance. Considering the multi-physics nature of the problem, ...
    • Mathematical and Numerical Analysis of Flow in Deformable Porous Media 

      Both, Jakub Wiktor (Doctoral thesis, 2019-11-27)
      This dissertation focuses on the mathematical analysis and numerical solution of coupled deformation- and flow-related processes in porous media, modeled by the theory of poro-elasticity. It comprises contributions within ...
    • On the rate of convergence of alternating minimization for non-smooth non-strongly convex optimization in Banach spaces 

      Both, Jakub Wiktor (Journal article; Peer reviewed, 2022)
      In this paper, the convergence of the fundamental alternating minimization is established for non-smooth non-strongly convex optimization problems in Banach spaces, and novel rates of convergence are provided. As objective ...