High order immersed hybridized difference methods for elliptic interface problems

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Finite difference methods for boundary value problems involving PDEs (65N06)

Cites Work

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Hybrid difference methods for PDEs
Hybrid spectral difference methods for an elliptic equation
A correction function method for Poisson problems with interface jump conditions
On the fictitious-domain and interpolation formulations of the matched interface and boundary (MIB) method
An immersed boundary method with formal second-order accuracy and reduced numerical viscosity
High order solution of Poisson problems with piecewise constant coefficients and interface jumps
An immersed hybrid difference method for the elliptic interface equation
A high order compact finite difference scheme for elliptic interface problems with discontinuous and high-contrast coefficients
Sixth order compact finite difference schemes for Poisson interface problems with singular sources
A novel hybrid difference method for an elliptic equation
A kernel-free boundary integral method for elliptic boundary value problems
High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources
An enriched immersed finite element method for interface problems with nonhomogeneous jump conditions
IMMERSED BOUNDARY METHODS
The immersed boundary method
The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
The extended finite element method (XFEM) for solidification problems
An immersed finite element space and its approximation capability
Convergence analysis of the immersed interface method
A Higher Degree Immersed Finite Element Method Based on a Cauchy Extension for Elliptic Interface Problems
A Kernel-Free Boundary Integral Method for Variable Coefficients Elliptic PDEs
The Immersed Interface Method
The Immersed Interface Hybridized Difference Method for Parabolic Interface Problems

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