A study on moving mesh finite element solution of the porous medium equation
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Publication:680217
DOI10.1016/j.jcp.2016.11.045zbMath1378.76110arXiv1605.03570OpenAlexW2347539535MaRDI QIDQ680217
Publication date: 22 January 2018
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1605.03570
finite element methodporous medium equationfree boundaryimmersed boundaryadaptive moving mesh methodHessian-based adaptivitymoving mesh PDE method
Flows in porous media; filtration; seepage (76S05) Finite element methods applied to problems in fluid mechanics (76M10)
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Uses Software
Cites Work
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- Numerical study of the porous medium equation with absorption, variable exponents of nonlinearity and free boundary
- Full discretization of the porous medium/fast diffusion equation based on its very weak formulation
- Adaptive moving mesh methods
- Numerical simulation for porous medium equation by local discontinuous Galerkin finite element method
- A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions
- Monotone finite volume schemes for diffusion equations on polygonal meshes
- Interfaces in multidimensional diffusion equations with absorption terms
- Variational mesh adaptation. II: Error estimates and monitor functions
- A geometric discretization and a simple implementation for variational mesh generation and adaptation
- Maximum-principle-satisfying second order discontinuous Galerkin schemes for convection-diffusion equations on triangular meshes
- Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes
- Study of the solutions to a model porous medium equation with variable exponent of nonlinearity
- A moving mesh finite element algorithm for the adaptive solution of time-dependent partial differential equations with moving boundaries
- Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions
- How a Nonconvergent Recovered Hessian Works in Mesh Adaptation
- R-Adaptive Reconnection-based Arbitrary Lagrangian Eulerian Method-R-ReALE
- The Behavior of the Support of Solutions of the Equation of Nonlinear Heat Conduction with Absorption in One Dimension
- Solving Ordinary Differential Equations I
- Adaptivity with moving grids
- Finite Element Approximation of the Fast Diffusion and the Porous Medium Equations
- Moving Finite Elements. I
- Numerical Methods for Flows Through Porous Media. I
- Approximation of Degenerate Parabolic Problems Using Numerical Integration
- Temporal Derivatives in the Finite-Element Method on Continuously Deforming Grids
- A new approach to grid generation
- Regularity of the free boundary for the porous medium equation
- A priori 𝐿^{𝜌} error estimates for Galerkin approximations to porous medium and fast diffusion equations
- Self–similar numerical solutions of the porous–medium equation using moving mesh methods
- Moving Mesh Partial Differential Equations (MMPDES) Based on the Equidistribution Principle
- Error Estimates for a Class of Degenerate Parabolic Equations
- Velocity-Based Moving Mesh Methods for Nonlinear Partial Differential Equations
- On the mesh nonsingularity of the moving mesh PDE method
- A moving mesh finite element algorithm for fluid flow problems with moving boundaries
- A Moving Mesh Method Based on the Geometric Conservation Law
- Optimal Rates of Convergence for Degenerate Parabolic Problems in Two Dimensions
- Monotone Finite Difference Schemes for Anisotropic Diffusion Problems via Nonnegative Directional Splittings
- Convergence of the Finite Element Method for the Porous Media Equation with Variable Exponent
- Two-step error estimators for implicit Runge--Kutta methods applied to stiff systems
- Parabolic Monge–Ampère methods for blow-up problems in several spatial dimensions
- Convergent Difference Schemes for Degenerate Elliptic and Parabolic Equations: Hamilton--Jacobi Equations and Free Boundary Problems
- Regularity Propeties of Flows Through Porous Media
- An arbitrary Lagrangian-Eulerian computing method for all flow speeds
- Moving mesh methods in multiple dimensions based on harmonic maps
- Variational mesh adaptation: Isotropy and equidistribution
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