Analysis and Approximation of Mixed-Dimensional PDEs on 3D-1D Domains Coupled with Lagrange Multipliers

DOI10.1137/20M1329664zbMath1460.35109arXiv2004.02722OpenAlexW3133338453WikidataQ114074206 ScholiaQ114074206MaRDI QIDQ5855632

Miroslav Kuchta, Paolo Zunino, Federica Laurino, Kent-André Mardal

Publication date: 19 March 2021

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.02722

zbMATH Keywords

existence of solutionsfinite element approximationcombination of Dirichlet and Neumann conditionsmixed-dimensional PDEs

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) 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)

Related Items (8)

3D-1D coupling on non conforming meshes via a three-field optimization based domain decomposition ⋮ Reduced Lagrange multiplier approach for non-matching coupling of mixed-dimensional domains ⋮ Linking discrete and continuum diffusion models: Well‐posedness and stable finite element discretizations ⋮ Rational approximation preconditioners for multiphysics problems ⋮ An optimization based 3D-1D coupling strategy for tissue perfusion and chemical transport during tumor-induced angiogenesis ⋮ A PDE-constrained optimization method for 3D-1D coupled problems with discontinuous solutions ⋮ Assembly of Multiscale Linear PDE Operators ⋮ Improving Neural Simulations with the EMI Model

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