Error Estimates for the Gradient Discretisation Method on Degenerate Parabolic Equations of Porous Medium Type

DOI10.1007/978-3-030-69363-3_2zbMath1470.76097OpenAlexW3016306668MaRDI QIDQ5153007

Gianmarco Manzini, Jérôme Droniou, Clément Cancès, Manuela Bastidas Olivares, Iuliu Sorin Pop, Cindy Guichard

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_2

zbMATH Keywords

error estimatesnumerical testsdiscontinuous Galerkin methodporous medium equationfast diffusionvirtual element methodslow diffusiongradient discretisation methodpolytopal methodshybrid mimetic mixed methodvertex approximate gradient method

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Finite element methods applied to problems in fluid mechanics (76M10)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Uniform-in-time convergence of numerical methods for non-linear degenerate parabolic equations
• On the time continuity of entropy solutions
• A combined finite volume-nonconforming/mixed-hybrid finite element scheme for degenerate parabolic problems
• Error estimates for the finite volume discretization for the porous medium equation
• Analysis of \(hp\) discontinuous Galerkin methods for incompressible two-phase flow
• Quasilinear elliptic-parabolic differential equations
• The Stefan problem. Translated from the Russian by Marek Niezgódka and Anna Crowley
• Entropy solutions for nonlinear degenerate problems
• A third Strang lemma and an Aubin-Nitsche trick for schemes in fully discrete formulation
• A study on iterative methods for solving Richards' equation
• The gradient discretisation method
• A posteriori error estimates, stopping criteria, and adaptivity for two-phase flows
• Numerical analysis of a robust free energy diminishing finite volume scheme for parabolic equations with gradient structure
• \(L^ 1\)-contraction and uniqueness for quasilinear elliptic-parabolic equations
• Mixed finite elements for the Richards' equation: linearization procedure
• A finite volume method on general meshes for a degenerate parabolic convection-reaction-diffusion equation
• A modified L-scheme to solve nonlinear diffusion problems
• A unified approach to the Hölder regularity of solutions to degenerate and singular parabolic equations
• The hybrid high-order method for polytopal meshes. Design, analysis, and applications
• A nonlinear time compactness result and applications to discretization of degenerate parabolic-elliptic PDEs
• Error estimates for a mixed finite element discretization of some degenerate parabolic equations
• Convergence of a nonlinear entropy diminishing Control Volume Finite Element scheme for solving anisotropic degenerate parabolic equations
• GRADIENT SCHEMES: A GENERIC FRAMEWORK FOR THE DISCRETISATION OF LINEAR, NONLINEAR AND NONLOCAL ELLIPTIC AND PARABOLIC EQUATIONS
• An a posteriori error estimate for vertex-centered finite volume discretizations of immiscible incompressible two-phase flow
• REGULARIZATION SCHEMES FOR DEGENERATE RICHARDS EQUATIONS AND OUTFLOW CONDITIONS
• The Gradient Discretization Method for Slow and Fast Diffusion Porous Media Equations
• Finite-Element Approximation of the Nonstationary Navier–Stokes Problem. Part IV: Error Analysis for Second-Order Time Discretization
• Convergence of MPFA on triangulations and for Richards' equation
• Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems
• Energy error estimates for a linear scheme to approximate nonlinear parabolic problems
• Approximation of Degenerate Parabolic Problems Using Numerical Integration
• Finite volumes and nonlinear diffusion equations
• Mixed finite elements and Newton-type linearizations for the solution of Richards' equation
• Finite Element Approximation of The Transport of Reactive Solutes in Porous Media. Part II: Error Estimates for Equilibrium Adsorption Processes
• A robust, mass conservative scheme for two-phase flow in porous media including Hölder continuous nonlinearities
• Interior and Boundary Continuity of Weak Solutions of Degenerate Parabolic Equations
• 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
• Improving Newton's Method Performance by Parametrization: The Case of the Richards Equation
• Finite volume schemes for diffusion equations: Introduction to and review of modern methods
• High-order Mass-lumped Schemes for Nonlinear Degenerate Elliptic Equations
• Mathematical study of a petroleum-engineering scheme

This page was built for publication: Error Estimates for the Gradient Discretisation Method on Degenerate Parabolic Equations of Porous Medium Type