Heterogeneous Stefan problem and permafrost models with P0-P0 finite elements and fully implicit monolithic solver

DOI10.3934/era.2022078OpenAlexW4293202862WikidataQ114022600 ScholiaQ114022600MaRDI QIDQ2127575

Naren Vohra, Małgorzata Peszyńska, Lisa Bigler

Publication date: 20 April 2022

Published in: Electronic Research Archive (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/era.2022078

zbMATH Keywords

mixed finite element methodsStefan problemfree boundary problemspermafrostheterogeneous coefficientsnonlinear parabolic partial differential equationsemismooth Newton solver

Mathematics Subject Classification ID

Mechanics of deformable solids (74-XX) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx)

Uses Software

• engineering toolbox

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Compatible algorithms for coupled flow and transport
• The Stefan problem in heterogeneous media
• A generalized Stefan problem in several space variables
• Pore-to-core simulations of flow with large velocities using continuum models and imaging data
• Error estimates for a semi-explicit numerical scheme for Stefan-type problems
• A variational inequality approach to generalized two-phase Stefan problem in several space variables
• Mathematical and numerical models for coupling surface and groundwater flows
• A priori error estimates for a mixed finite element discretization of the Richard's equation
• Theory and practice of finite elements.
• Coupled flow and biomass-nutrient growth at pore-scale with permeable biofilm, adaptive singularity and multiple species
• A reduced fracture model for two-phase flow with different rock types
• Stability of a numerical scheme for methane transport in hydrate zone under equilibrium and non-equilibrium conditions
• Evolution of phase transitions in methane hydrate
• Homogenization and porous media
• A comparison of numerical models for one-dimensional Stefan problems
• Advection of methane in the hydrate zone: model, analysis and examples
• Nonlinear Degenerate Evolution Equations in Mixed Formulation
• Numerical solution of the nonlinear heat equation in heterogeneous media¹
• Solution of the time discretized Stefan problem by Newton's method
• The combined use of a nonlinear chernoff formula with a regularization procedure for two-phase stefan problems
• Energy error estimates for a linear scheme to approximate nonlinear parabolic problems
• On Convergence of Block-Centered Finite Differences for Elliptic Problems
• Finite element approximations of singular parabolic problems
• The Alternating Phase Truncation Method for Numerical Solution of a Stefan Problem
• Mixed and Hybrid Finite Element Methods
• The Cahn–Hilliard gradient theory for phase separation with non-smooth free energy Part I: Mathematical analysis
• AP¹--P¹Finite Element Method for a Phase Relaxation Model I: Quasi-Uniform Mesh
• Error Estimates for the Multidimensional Two-Phase Stefan Problem
• Optimal Rates of Convergence for Degenerate Parabolic Problems in Two Dimensions
• A Nonlinear Mixed Finite Element Method for a Degenerate Parabolic Equation Arising in Flow in Porous Media
• Mixed Finite Element Methods and Applications
• Analysis of Expanded Mixed Finite Element Methods for a Nonlinear Parabolic Equation Modeling Flow into Variably Saturated Porous Media
• PREMELTING DYNAMICS
• Multidimensional Stefan Problems