Two finite element approaches for the porous medium equation that are positivity preserving and energy stable
DOI10.1007/S10915-024-02642-XzbMATH Open1547.65149MaRDI QIDQ6608068
Arjun Vijaywargiya, Guosheng Fu
Publication date: 19 September 2024
Published in: Journal of Scientific Computing (Search for Journal in Brave)
porous medium equationmixed finite element methodentropy stabilitylog-density formulationpositivity perservation
PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) Finite difference methods applied to problems in fluid mechanics (76M20) Stokes and related (Oseen, etc.) flows (76D07) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Tilings in (n) dimensions (aspects of discrete geometry) (52C22) Positive solutions to PDEs (35B09)
Cites Work
- Title not available (Why is that?)
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- Numerical simulation for porous medium equation by local discontinuous Galerkin finite element method
- A study on moving mesh finite element solution of the porous medium equation
- Energetically stable discretizations for charge transport and electrokinetic models
- Third order maximum-principle-satisfying direct discontinuous Galerkin methods for time dependent convection diffusion equations on unstructured triangular meshes
- Bound preserving and energy dissipative schemes for porous medium equation
- On Lagrangian schemes for porous medium type generalized diffusion equations: a discrete energetic variational approach
- Skew-selfadjoint form for systems of conservation laws
- A new finite element formulation for computational fluid dynamics. V: Circumventing the Babuška-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations
- On the symmetric form of systems of conservation laws with entropy
- Recherches théoriques sur l'écoulement des nappes d'eau infiltrées dans le sol et sur le débit des sources.
- A Lagrangian scheme for the solution of nonlinear diffusion equations using moving simplex meshes
- A numerical approach to degenerate parabolic equations
- Efficient, positive, and energy stable schemes for multi-d Poisson-Nernst-Planck systems
- High-order space-time finite element methods for the Poisson-Nernst-Planck equations: positivity and unconditional energy stability
- Numerical methods for porous medium equation by an energetic variational approach
- A moving mesh finite element algorithm for the adaptive solution of time-dependent partial differential equations with moving boundaries
- Higher order triangular finite elements with mass lumping for the wave equation
- THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
- An explicit finite-difference scheme for one-dimensional generalized porous medium equations: interface tracking and the hole filling problem
- The Finite Element Method: Theory, Implementation, and Applications
- High Order Finite Difference WENO Schemes for Nonlinear Degenerate Parabolic Equations
- How an Initially Stationary Interface Begins to Move in Porous Medium Flow
- Variational particle schemes for the porous medium equation and for the system of isentropic Euler equations
- An Interface Tracking Algorithm for the Porous Medium Equation
- A coordinate transformation for the porous media equation that renders the free boundary stationary
- Evolution of self-similarity, and other properties of waiting-time solutions of the porous medium equation: the case of viscous gravity currents
- Diffusive Relaxation Schemes for Multiscale Discrete-Velocity Kinetic Equations
- A monotone finite element scheme for convection-diffusion equations
- New Higher-Order Mass-Lumped Tetrahedral Elements for Wave Propagation Modelling
- A numerical treatment of a superdegenerate equation with applications to the porous media equation
- Connection between finite volume and mixed finite element methods
- Adaptive finite element solution of the porous medium equation in pressure formulation
- Convergence of the Finite Element Method for the Porous Media Equation with Variable Exponent
- A Finite Difference Approach to Some Degenerate Nonlinear Parabolic Equations
- DIFFUSION FROM AN INSTANTANEOUS POINT SOURCE WITH A CONCENTRATION-DEPENDENT COEFFICIENT
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