A generalized finite difference method for solving elliptic interface problems with non-homogeneous jump conditions on surfaces

PDEs with low regular coefficients and/or low regular data (35R05) Finite difference methods for boundary value problems involving PDEs (65N06) Boundary value problems on manifolds (58J32)

Cites Work

Unnamed Item
Unnamed Item
Arbitrary Lagrangian-Eulerian finite-element method for computation of two-phase flows with soluble surfactants
Solving second order non-linear elliptic partial differential equations using generalized finite difference method
Level set equations on surfaces via the closest point method
A finite volume method on general surfaces and its error estimates
The immersed interface method using a finite element formulation
Influence of several factors in the generalized finite difference method
Finite element methods and their convergence for elliptic and parabolic interface problems
Improvements of generalized finite difference method and comparison with other meshless method
New Cartesian grid methods for interface problems using the finite element formulation
Direct meshless local Petrov-Galerkin method for elliptic interface problems with applications in electrostatic and elastostatic
A finite element method for high-contrast interface problems with error estimates independent of contrast
A conforming enriched finite element method for elliptic interface problems
Solving elliptical equations in 3D by means of an adaptive refinement in generalized finite differences
An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
A boundary condition capturing method for Poisson's equation on irregular domains
A generalized finite difference method for solving Stokes interface problems
A spatially adaptive high-order meshless method for fluid-structure interactions
A generalized finite difference method for solving elliptic interface problems
A generalized finite difference method for solving elasticity interface problems
An extended mixed finite element method for elliptic interface problems
The local tangential lifting method for moving interface problems on surfaces with applications
High-order extended finite element methods for solving interface problems
An immersed finite element method for elliptic interface problems in three dimensions
A meshfree generalized finite difference method for surface PDEs
A fully Lagrangian meshfree framework for PDEs on evolving surfaces
Interpolating stabilized moving least squares (MLS) approximation for 2D elliptic interface problems
The finite element method for elliptic equations with discontinuous coefficients
A local tangential lifting differential method for triangular meshes
A meshless method based on the generalized finite difference method for three-dimensional elliptic interface problems
An immersed finite element method for elliptic interface problems on surfaces
A new intrinsic numerical method for PDE on surfaces
Discrete Conservation Laws on Curved Surfaces II: A Dual Approach
The extended/generalized finite element method: An overview of the method and its applications
The Implicit Closest Point Method for the Numerical Solution of Partial Differential Equations on Surfaces
The convergence of the bilinear and linear immersed finite element solutions to interface problems
A new multiscale finite element method for high-contrast elliptic interface problems
The immersed boundary method
An efficient meshfree point collocation moving least squares method to solve the interface problems with nonhomogeneous jump conditions
Moving least-squares approximation with discontinuous derivative basis functions for shell structures with slope discontinuities
Robust flux error estimation of an unfitted Nitsche method for high-contrast interface problems
An immersed finite element space and its approximation capability
Partially Penalized Immersed Finite Element Methods For Elliptic Interface Problems
Discrete Conservation Laws on Curved Surfaces
Finite element methods for surface PDEs
An extended finite element method with polygonal enrichment shape functions for crack propagation and stiff interfaceproblems