The Mixed Virtual Element Method for the Richards Equation

DOI10.1007/978-3-030-69363-3_7zbMath1470.76044OpenAlexW3172118528MaRDI QIDQ5153012

Sundararajan Natarajan, Gianmarco Manzini, Dibyendu Adak

Publication date: 28 September 2021

Published in: Polyhedral Methods in Geosciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-69363-3_7

zbMATH Keywords

convergence analysispolygonal meshmixed virtual element methodlow-order approximationRichard equation

Mathematics Subject Classification ID

Finite element methods applied to problems in fluid mechanics (76M10)

Cites Work

• \(H(\mathrm{div})\) and \(H(\mathbf{curl})\)-conforming virtual element methods
• Equivalent projectors for virtual element methods
• A high-order mimetic method on unstructured polyhedral meshes for the diffusion equation
• Virtual element methods for plate bending problems
• Mimetic finite difference method
• A hybrid mortar virtual element method for discrete fracture network simulations
• Multiscale mixed/mimetic methods on corner-point grids
• Quasilinear elliptic-parabolic differential equations
• Nonstationary filtration in partially saturated porous media
• Serendipity nodal VEM spaces
• The virtual element method for discrete fracture network simulations
• A posteriori error estimates for the virtual element method
• A virtual element method for contact
• Discontinuous skeletal gradient discretisation methods on polytopal meshes
• The virtual element method for eigenvalue problems with potential terms on polytopic meshes.
• Error estimates for a time discretization method for the Richards' equation
• Mixed finite elements for the Richards' equation: linearization procedure
• A priori error estimates for a mixed finite element discretization of the Richard's equation
• The finite volume method for Richards equation
• SUPG stabilization for the nonconforming virtual element method for advection-diffusion-reaction equations
• Extended virtual element method for the Laplace problem with singularities and discontinuities
• The conforming virtual element method for polyharmonic problems
• The \(p\)- and \(hp\)-versions of the virtual element method for elliptic eigenvalue problems
• A posteriori error estimation and adaptivity in \textit{hp} virtual elements
• Towards effective flow simulations in realistic discrete fracture networks
• The virtual element method for underground flow simulations in fractured media
• A virtual element method for elastic and inelastic problems on polytope meshes
• The mimetic finite difference method for elliptic problems
• Virtual Element Method for general second-order elliptic problems on polygonal meshes
• Mixed virtual element methods for general second order elliptic problems on polygonal meshes
• A plane wave virtual element method for the Helmholtz problem
• The nonconforming virtual element method
• The nonconforming virtual element method for plate bending problems
• Virtual Elements for Linear Elasticity Problems
• Basic principles of mixed Virtual Element Methods
• Hourglass stabilization and the virtual element method
• Virtual and smoothed finite elements: A connection and its application to polygonal/polyhedral finite element methods
• Divergence free virtual elements for the stokes problem on polygonal meshes
• Arbitrary-Order Nodal Mimetic Discretizations of Elliptic Problems on Polygonal Meshes
• Basic principles of hp virtual elements on quasiuniform meshes
• Virtual element methods for parabolic problems on polygonal meshes
• Mimetic finite differences for elliptic problems
• Approximation of Degenerate Parabolic Problems Using Numerical Integration
• Mixed finite elements and Newton-type linearizations for the solution of Richards' equation
• CAPILLARY CONDUCTION OF LIQUIDS THROUGH POROUS MEDIUMS
• Convergence Analysis of the mimetic Finite Difference Method for Elliptic Problems with Staggered Discretizations of Diffusion Coefficients
• The fully nonconforming virtual element method for biharmonic problems
• Order of Convergence Estimates for an Euler Implicit, Mixed Finite Element Discretization of Richards' Equation
• Conforming and nonconforming virtual element methods for elliptic problems
• Solution of doubly nonlinear and degenerate parabolic problems by relaxation schemes
• A Nonlinear Mixed Finite Element Method for a Degenerate Parabolic Equation Arising in Flow in Porous Media
• BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
• Analysis of Expanded Mixed Finite Element Methods for a Nonlinear Parabolic Equation Modeling Flow into Variably Saturated Porous Media
• The Hitchhiker's Guide to the Virtual Element Method
• New perspectives on polygonal and polyhedral finite element methods
• Post processing of solution and flux for the nodal mimetic finite difference method
• The nonconforming Virtual Element Method for eigenvalue problems
• Residuala posteriorierror estimation for the Virtual Element Method for elliptic problems
• A virtual element method for the Steklov eigenvalue problem
• A Parallel Solver for Large Scale DFN Flow Simulations
• Weather Prediction by Numerical Process
• A Stream Virtual Element Formulation of the Stokes Problem on Polygonal Meshes
• A virtual element method with arbitrary regularity
• Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes
• The NonConforming Virtual Element Method for the Stokes Equations
• A Posteriori Error Estimate for a PDE-Constrained Optimization Formulation for the Flow in DFNs
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item