h1

% IMPORTANT: The following is UTF-8 encoded.  This means that in the presence
% of non-ASCII characters, it will not work with BibTeX 0.99 or older.
% Instead, you should use an up-to-date BibTeX implementation like “bibtex8” or
% “biber”.

@PHDTHESIS{Boissere:1022300,
      author       = {Boisserée, Simon Melchior},
      othercontributors = {Bachmayr, Markus and Moulas, Evangelos and Thomas, Marita},
      title        = {{S}pace-time adaptive methods for poroviscoelastic flow
                      models},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      address      = {Aachen},
      publisher    = {RWTH Aachen University},
      reportid     = {RWTH-2025-09929},
      pages        = {1 Online-Ressource : Illustrationen},
      year         = {2025},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University 2026; Dissertation, RWTH Aachen University, 2025},
      abstract     = {In this work we consider a system of equations that arises
                      in geophysics when modeling subsurface flows of water,
                      magma, or gases such as CO2 in a poroviscoelastic medium. We
                      start by deriving the model equations in terms of porosity
                      and effective pressure before transforming them into a
                      nondimensional form. Furthermore, we state two simplified
                      models directly arising from the full viscoelastic model,
                      namely the viscous limit and low-porosity approximation. We
                      demonstrate that the analysis for the full model and the
                      low-porosity approximation can be unified due to a
                      transformation of variables, implying that it only remains
                      to show well-posedness for the viscous limit as a separate
                      case. We define a notion of solution that includes
                      discontinuous porosity distributions as they often occur in
                      nature at the interface between sedimentary layers. We
                      proceed by proving well-posedness of the viscoelastic model
                      and the viscous limit. We mainly follow the idea of
                      combining a fixed-point iteration for the porosity equation
                      with regularity theory for the equation modeling the
                      effective pressure. With this strategy, it turns out that in
                      the viscous limit a result allowing very general
                      discontinuous initial porosity distributions only follows if
                      we restrict ourselves to one- and two-dimensional domains.
                      However, by assuming that the initial porosity has a bounded
                      total variation and by using a compactness argument for
                      sequences of approximate solutions, we obtain existence of
                      solutions also in arbitrary dimensions. This includes all
                      practically relevant cases of discontinuous initial porosity
                      distributions. For the viscoelastic model, we use a similar
                      fixed-point argument as before. Here, we can prove existence
                      and uniqueness of solutions for discontinuous initial
                      porosity distributions, but only by assuming certain Hölder
                      regularity of the shape of the discontinuities as well as
                      Hölder smoothness of the initial functions away from the
                      discontinuities. Using the same fixed-point formulation as
                      before, we introduce an adaptive space-time method to solve
                      the viscoelastic model numerically. This method can also be
                      modified slightly to cover the viscous limit as well.
                      Furthermore, we prove convergence and a posteriori error
                      bounds for this approach. Then, we present some numerical
                      tests for geophysically relevant problem settings. For these
                      tests, we show numerically that our methods generate
                      quasi-optimal approximations of the corresponding analytical
                      solutions, independent of the presence of a discontinuity.
                      As a geophysical application, we discuss the coupling of our
                      method with a chemical transport problem since it provides
                      new insights into the formation of chemical anomalies,
                      which, for example, can lead to the formation of ore
                      deposits in the Earth's subsurface. Then, we briefly discuss
                      other possible space-time adaptive approaches to solving the
                      model problem. Next, we compare our approach with a finite
                      difference scheme, where it turns out that this method only
                      reaches low convergence rates for discontinuous porosity
                      distributions. Finally, we show some further advantages of
                      space-time methods for solving related inverse problems. We
                      present two different approaches that attempt to invert a
                      simplified model problem.},
      cin          = {111410 / 110000},
      ddc          = {510},
      cid          = {$I:(DE-82)111410_20170801$ / $I:(DE-82)110000_20140620$},
      pnm          = {DFG project G:(GEPRIS)442047500 - SFB 1481: Sparsity und
                      singuläre Strukturen (442047500)},
      pid          = {G:(GEPRIS)442047500},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2025-09929},
      url          = {https://publications.rwth-aachen.de/record/1022300},
}