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Immersed finite element methods for parabolic equations with moving interface

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Highly accurate biomolecular electrostatics in continuum dielectric environments
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Three‐dimensional immersed finite element methods for electric field simulation in composite materials
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An immersed finite element space and its approximation capability
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The convergence of the bilinear and linear immersed finite element solutions to interface problems
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The Embedded Curved Boundary Method for Orthogonal Simulation Meshes
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A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains
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Qualitative mathematical analysis of the Richards equation
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Flow patterns around heart valves
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New Cartesian grid methods for interface problems using the finite element formulation
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Finite element methods and their convergence for elliptic and parabolic interface problems
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Composite Finite Elements for Elliptic Boundary Value Problems with Discontinuous Coefficients
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Optimal convergence analysis of an immersed interface finite element method
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Flow patterns around heart valves: A numerical method
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A p-th degree immersed finite element for boundary value problems with discontinuous coefficients
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High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources
inferredcites →https://doi.org/10.1016/j.jcp.2006.03.027openalex-snapshot
On the fictitious-domain and interpolation formulations of the matched interface and boundary (MIB) method
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The immersed interface method using a finite element formulation
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Developments in Cartesian cut cell methods
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An immersed finite element method for elasticity equations with interfaces
inferredcites →https://doi.org/10.1090/s0025-5718-99-01085-6openalex-snapshot
Can a finite element method perform arbitrarily badly?
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Modeling Electrostatic Levitation of Dust Particles on Lunar Surface
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Immersed-Interface Finite-Element Methods for Elliptic Interface Problems with Nonhomogeneous Jump Conditions
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Multidimensional Stefan Problems
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The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
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A Trilinear Immersed Finite Element Method for Solving the Electroencephalography Forward Problem
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Immersed Interface Methods for Neumann and Related Problems in Two and Three Dimensions
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Application of the Method of Lines to Parabolic Partial Differential Equations With Error Estimates
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A Multi-Boundary Stefan Problem and the Disappearance of Phases
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Error estimation of a class of quadratic immersed finite element methods for elliptic interface problems
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Immersed Finite Element Methods for Elliptic Interface Problems with Non-Homogeneous Jump Conditions
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A compendium of partial differential equation models: method of lines analysis with Matlab

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Material Design Using Topology Optimization with Immersed Interface Fem
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Three‐dimensional immersed finite‐element method for anisotropic magnetostatic/electrostatic interface problems with nonhomogeneous flux jump
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Partially penalized immersed finite element methods for parabolic interface problems
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Long‐time stability and asymptotic analysis of the IFE method for the multilayer porous wall model
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Numerical simulation of one-dimensional parabolic problems with moving interfaces by using two second order time-stepping schemes in SGFEM
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Superconvergence analysis for nonlinear parabolic equation with $$EQ_1^\mathrm{{rot}}$$ E Q 1 rot nonconforming finite element
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Long time error estimates of IFE methods for the unsteady multi-layer porous wall model
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Construction of discontinuous enrichment functions for enriched or generalized FEM’s for interface elliptic problems in 1D
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A fully decoupled iterative method with three-dimensional anisotropic immersed finite elements for Kaufman-type discharge problems
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The Frenet immersed finite element method for elliptic interface problems: An error analysis
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A Huygens immersed-finite-element particle-in-cell method for modeling plasma-surface interactions with moving interface
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Unconditional stability and convergence of second-order backward differentiation formula in SGFEM for parabolic interface problems
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An implicit particle-in-cell model based on anisotropic immersed-finite-element method
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An iterative immersed finite element method for an electric potential interface problem based on given surface electric quantity
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Superconvergence analysis for a nonlinear parabolic equation with a BDF finite element method
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Numerical study of the radio-frequency biased accelerating system in ion thrusters
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Immersed finite element method of lines for moving interface problems with nonhomogeneous flux jump
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Variational data assimilation with finite-element discretization for second-order parabolic interface equation
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A Coupled Multiphysics Model and a Decoupled Stabilized Finite Element Method for the Closed-Loop Geothermal System
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Solving Parabolic Moving Interface Problems with Dynamical Immersed Spaces on Unfitted Meshes: Fully Discrete Analysis
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PIFE-PIC: Parallel Immersed Finite Element Particle-in-Cell for 3-D Kinetic Simulations of Plasma-Material Interactions
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Space-Time FEM-BEM Couplings for Parabolic Transmission Problems
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Immersed finite element method for heat transfer analysis in multi-layered thermal protection systems
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Kinetic Particle Simulations of Plasma Charging at Lunar Craters Under Severe Conditions
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Trilinear Immersed-Finite-Element Method for Three-Dimensional Anisotropic Interface Problems in Plasma Thrusters
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Partially Penalized Anisotropic Trilinear IFE-PIC Methods for DC Plasma Transport Problems
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Setochno-kharakteristicheskiy metod povyshennogo poryadka dlya sistem giperbolicheskikh uravneniy s kusochno-postoyannymi koeffitsientami
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A conforming-nonconforming mixed immersed finite element method for unsteady Stokes equations with moving interfaces
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The ADI difference and extrapolation scheme for high-dimensional variable coefficient evolution equations
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A Method of Lines Based on Immersed Finite Elements for Parabolic Moving Interface Problems
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An Immersed Finite Element Method for the Elasticity Problems with Displacement Jump
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An Immersed Finite Element Method for Elliptic Interface Problems with Multi-Domain and Triple Junction Points
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Immersed Finite Element Method for Interface Problems with Algebraic Multigrid Solver
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A New Finite Element for Interface Problems Having Robin Type Jump
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Linear and Quadratic Immersed Finite Element Methods for the Multi-Layer Porous Wall Model for Coronary Drug-Eluting Stents
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Improved Error Estimation for the Partially Penalized Immersed Finite Element Methods for Elliptic Interface Problems
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Error Analysis of an Immersed Finite Element Method for Time-Dependent Beam Interface Problems
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A $P_2$-$P_1$ Partially Penalized Immersed Finite Element Method for Stokes Interface Problems
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A Finite Difference Method for Elliptic Problems with Implicit Jump Condition
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High-Order Enriched Finite Element Methods for Elliptic Interface Problems with Discontinuous Solutions
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Numerical Analysis of Partially Penalized Immersed Finite Element Methods for Hyperbolic Interface Problems
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PPIFE Method with Non-Homogeneous Flux Jump Conditions and Its Efficient Numerical Solver for Elliptic Optimal Control Problems with Interfaces
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A Trilinear Immersed Finite Element Method for Solving Elliptic Interface Problems
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