A Posteriori Error Estimate for a PDE-Constrained Optimization Formulation for the Flow in DFNs

DOI10.1137/15M1014760zbMath1382.76159OpenAlexW2257087572MaRDI QIDQ5745016

Andrea Borio, Stefano Scialò, Stefano Berrone

Publication date: 11 February 2016

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

Full work available at URL: https://doi.org/10.1137/15m1014760

zbMATH Keywords

PDE-constrained optimizationdiscrete fracture networkssingle-phase flows``a posteriori error estimates

Mathematics Subject Classification ID

Hydrology, hydrography, oceanography (86A05) Flows in porous media; filtration; seepage (76S05) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Computational methods for problems pertaining to geophysics (86-08)

Related Items (17)

A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem ⋮ Conforming virtual element approximations of the two-dimensional Stokes problem ⋮ Uncertainty quantification analysis in discrete fracture network flow simulations ⋮ Flow simulations in porous media with immersed intersecting fractures ⋮ Comparison of the response to geometrical complexity of methods for unstationary simulations in discrete fracture networks with conforming, polygonal, and non-matching grids ⋮ A reduced basis method for a PDE-constrained optimization formulation in discrete fracture network flow simulations ⋮ The Mixed Virtual Element Method for the Richards Equation ⋮ SUPG stabilization for the nonconforming virtual element method for advection-diffusion-reaction equations ⋮ Reliable a posteriori mesh adaptivity in discrete fracture network flow simulations ⋮ Advanced computation of steady-state fluid flow in discrete fracture-matrix models: FEM-BEM and VEM-VEM fracture-block coupling ⋮ A virtual element method for the miscible displacement of incompressible fluids in porous media ⋮ An optimization approach for flow simulations in poro-fractured media with complex geometries ⋮ Machine learning for flux regression in discrete fracture networks ⋮ Non-stationary transport phenomena in networks of fractures: effective simulations and stochastic analysis ⋮ A residual a posteriori error estimate for the Virtual Element Method ⋮ Parallel Meshing, Discretization, and Computation of Flow in Massive Discrete Fracture Networks ⋮ Fast and robust flow simulations in discrete fracture networks with gpgpus

Uses Software

• SIDNUR

Cites Work

• An optimization approach for large scale simulations of discrete fracture network flows
• Guaranteed and fully robust a posteriori error estimates for conforming discretizations of diffusion problems with discontinuous coefficients
• A hybrid mortar virtual element method for discrete fracture network simulations
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• A posteriori error estimation and adaptive mesh-refinement techniques
• The virtual element method for discrete fracture network simulations
• Uncertainty quantification in discrete fracture network models: stochastic fracture transmissivity
• A Generalized Mixed Hybrid Mortar Method for Solving Flow in Stochastic Discrete Fracture Networks
• A Mortar BDD Method for Solving Flow in Stochastic Discrete Fracture Networks
• A mixed hybrid Mortar method for solving flow in discrete fracture networks
• A Posteriori Error Estimates Including Algebraic Error and Stopping Criteria for Iterative Solvers
• A New Approach to Simulating Flow in Discrete Fracture Networks with an Optimized Mesh
• Flow Simulation in Three-Dimensional Discrete Fracture Networks
• A Parallel Solver for Large Scale DFN Flow Simulations
• On Simulations of Discrete Fracture Network Flows with an Optimization-Based Extended Finite Element Method
• A PDE-Constrained Optimization Formulation for Discrete Fracture Network Flows
• High-order stochastic simulation of complex spatially Distributed natural phenomena
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