A Nitsche-based cut finite element solver for two-phase Stefan problems

Basic methods in fluid mechanics (76Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Thermodynamics and heat transfer (80Axx)

Cites Work

Ghost penalty
Finite element methods with symmetric stabilization for the transient convection-diffusion-reaction equation
Three-dimensional anisotropic mesh adaptation for phase change problems
Edge stabilization for Galerkin approximations of convection-diffusion-reaction problems
Approximate boundary-flux calculations
A numerical scheme for the Stefan problem on adaptive Cartesian grids with supralinear convergence rate
Modelling dendritic solidification with melt convection using the extended finite element method
Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
The fast construction of extension velocities in level set methods
Computation of dendrites using a phase field model
Superconvergence analysis of approximate boundary-flux calculations
A level set approach for computing solutions to incompressible two-phase flow
A simple level set method for solving Stefan problems
The partition of unity finite element method: basic theory and applications
Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows
Anisotropic mesh adaptation for the solution of the Stefan problem.
Stefan problem through extended finite elements: review and further investigations
Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids
Solving thermal and phase change problems with the extended finite element method
An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
Implementation of an X-FEM solver for the classical two-phase Stefan problem
A CutFEM method for two-phase flow problems
A cut finite element method for incompressible two-phase Navier-Stokes flows
Shape optimization using the cut finite element method
A finite element based level set method for two-phase incompressible flows
Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
An eXtended Finite Element Method/Lagrange multiplier based approach for fluid-structure interaction
CutFEM: Discretizing geometry and partial differential equations
A Penalty-Free Nonsymmetric Nitsche-Type Method for the Weak Imposition of Boundary Conditions
An adaptive finite element method for two-phase Stefan problems in two space dimensions. I. Stability and error estimates
On time integration in the XFEM
An efficient finite element method for embedded interface problems
A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method
Numerical Studies of Discrete Approximations to the Allen–Cahn Equation in the Sharp Interface Limit
An enthalpy method for convection/diffusion phase change
An Enthalpty Formulation of the Stefan Problem
The extended finite element method (XFEM) for solidification problems
CutFEM Method for Stefan--Signorini Problems with Application in Pulsed Laser Ablation
A penalty-free Nitsche method for the weak imposition of boundary conditions in compressible and incompressible elasticity
A finite element method for crack growth without remeshing
Fictitious domain methods using cut elements: III. A stabilized Nitsche method for Stokes’ problem
On strategies for enforcing interfacial constraints and evaluating jump conditions with the extended finite element method
A moving mesh finite element method for the solution of two-dimensional Stefan problems
Front-tracking finite element method for dendritic solidification

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