Well-Posedness and Discretization for a Class of Models for Mixed-Dimensional Problems with High-Dimensional Gap
DOI10.1137/20M1362541zbMath1478.65127arXiv2006.12273OpenAlexW3205402000MaRDI QIDQ5164710
Erlend Hodneland, Xiaozhe Hu, Jan Martin Nordbotten
Publication date: 12 November 2021
Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2006.12273
Flows in porous media; filtration; seepage (76S05) Error bounds for boundary value problems involving PDEs (65N15) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Physiological flows (76Z05) Physiological flow (92C35) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Finite volume methods for boundary value problems involving PDEs (65N08)
Uses Software
Cites Work
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- Modeling tissue perfusion in terms of 1d-3d embedded mixed-dimension coupled problems with distributed sources
- Multigrid method for \(H\text{(div)}\) in three dimensions
- Error analysis of piecewise constant pressure approximations of Darcy's law
- Functional analysis and exterior calculus on mixed-dimensional geometries
- A Local Error Estimate for the Poisson Equation with a Line Source Term
- ON THE COUPLING OF 1D AND 3D DIFFUSION-REACTION EQUATIONS: APPLICATION TO TISSUE PERFUSION PROBLEMS
- Mixed and Hybrid Finite Element Methods
- Mathematical modeling, analysis and numerical approximation of second-order elliptic problems with inclusions
- Robust Discretization of Flow in Fractured Porous Media
- A fast marching level set method for monotonically advancing fronts.
- Connection between finite volume and mixed finite element methods
- Mixed Finite Element Methods and Applications
- Splitting method for elliptic equations with line sources
- Non-local network dynamics via fractional graph Laplacians
- A hybrid discrete–continuum approach for modelling microcirculatory blood flow
- Derivation and analysis of coupled PDEs on manifolds with high dimensionality gap arising from topological model reduction
- Pulse Wave Propagation in the Arterial Tree
- Mixed Methods for Two-Phase Darcy--Stokes Mixtures of Partially Melted Materials with Regions of Zero Porosity
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