• Analysis and Approximation of Coupled 1D-3D Flow Models 

      Gjerde, Ingeborg Gåseby (Doctoral thesis, 2020-03-18)
      In this thesis, we consider a specific instance of mixed-dimensional partial differential equations (PDEs) commonly referred to as the coupled 1D-3D flow model. The model itself consists of the Poisson equation defined on ...
    • A Mixed Approach to the Poisson Problem with Line Sources 

      Gjerde, Ingeborg Gåseby; Kumar, Kundan; Nordbotten, Jan Martin (Journal article; Peer reviewed, 2021)
      In this work we consider the dual-mixed variational formulation of the Poisson equation with a line source. The analysis and approximation of this problem is nonstandard, as the line source causes the solutions to be ...
    • A singularity removal method for coupled 1D–3D flow models 

      Gjerde, Ingeborg Gåseby; Kumar, Kundan; Nordbotten, Jan Martin (Journal article; Peer reviewed, 2019)
      In reservoir simulations, the radius of a well is inevitably going to be small compared to the horizontal length scale of the reservoir. For this reason, wells are typically modelled as lower-dimensional sources. In this ...