Finite element methods for flow in porous media

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Perustieteiden korkeakoulu | Doctoral thesis (article-based)
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Verkkokirja (890 KB, 33 s.)
Aalto University publication series DOCTORAL DISSERTATIONS , 103/2011
This thesis studies the application of finite element methods to porous flow problems. Particular attention is paid to locally mass conserving methods, which are very well suited for typical multiphase flow applications in porous media. The focus is on the Brinkman model, which is a parameter dependent extension of the classical Darcy model for porous flow taking the viscous phenomena into account. The thesis introduces a mass conserving finite element method for the Brinkman flow, with complete mathematical analysis of the method. In addition, stochastic material parameters are considered for the Brinkman flow, and parameter dependent Robin boundary conditions for the underlying Darcy flow. All of the theoretical results in the thesis are also verified with extensive numerical testing. Furthermore, many implementational aspects are discussed in the thesis, and computational viability of the methods introduced, both in terms of usefulness and computational complexity, is taken into account.
Supervising professor
Stenberg, Rolf, Prof.
Thesis advisor
Stenberg, Rolf, Prof.
finite element methods, porous media, Brinkman model, a posteriori error estimates
Other note
  • [Publication 1]: Juho Könnö, Dominik Schötzau and Rolf Stenberg. Mixed Finite Element Methods for Problems with Robin Boundary Conditions. SIAM Journal on Numerical Analysis, 49(1), pp. 285-308, 2011.
  • [Publication 2]: Juho Könnö and Rolf Stenberg. Analysis of H(div)-conforming Finite Elements for the Brinkman Problem. Accepted for publication in Mathematical Models and Methods in Applied Sciences, doi:10.1142/S0218202511005726, 2011.
  • [Publication 3]: Juho Könnö and Rolf Stenberg. Numerical Computations with H(div)-Finite Elements for the Brinkman Problem. Accepted for publication in Computational Geosciences, doi:10.1007/s10596-011-9259-x, Preprint: arXiv:1103.5338v1 2011.
  • [Publication 4]: Claude Gittelson, Juho Könnö, Christoph Schwab and Rolf Stenberg. The Multi-Level Monte Carlo Finite Element Method for the Stochastic Brinkman Problem. Submitted to Numerische Mathematik, Preprint: ETH Zürich, Seminar für Angewandte Mathematik, Research Report 2011-31, 2011.