A sharp interface finite volume method for elliptic equations on Cartesian grids
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Publication:834072
DOI10.1016/j.jcp.2009.04.018zbMath1169.65343OpenAlexW2155704971MaRDI QIDQ834072
C. Scharfenberg, Rupert Klein, Michael Oevermann
Publication date: 19 August 2009
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jcp.2009.04.018
finite volume methodselliptic equationsdiscontinuous solutionembedded interfacevariable and discontinuous coefficients
Boundary value problems for second-order elliptic equations (35J25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)
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Uses Software
Cites Work
- Unnamed Item
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- Unnamed Item
- Discretization of Dirac delta functions in level set methods
- A numerical method for solving variable coefficient elliptic equation with interfaces
- A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains, with applications to the Stefan problem
- On the fictitious-domain and interpolation formulations of the matched interface and boundary (MIB) method
- A Cartesian grid finite volume method for elliptic equations with variable coefficients and embedded interfaces
- An extended pressure finite element space for two-phase incompressible flows with surface tension
- Numerical analysis of blood flow in the heart
- A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
- Finite element methods and their convergence for elliptic and parabolic interface problems
- Regularization techniques for numerical approximation of PDEs with singularities
- New Cartesian grid methods for interface problems using the finite element formulation
- The blob projection method for immersed boundary problems
- A Lagrange multiplier method for the finite element solution of elliptic interface problems using non-matching meshes
- Extension of finite volume compressible flow solvers to multi-dimensional, variable density zero Mach number flows
- Level set methods and dynamic implicit surfaces
- Three-dimensional elliptic solvers for interface problems and applications
- An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
- Numerical approximations of singular source terms in differential equations
- A boundary condition capturing method for Poisson's equation on irregular domains
- Stability of a Cartesian grid projection method for zero Froude number shallow water flows
- Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities
- A fourth-order auxiliary variable projection method for zero-Mach number gas dynamics
- High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources
- Arbitrary discontinuities in finite elements
- Maximum Principle Preserving Schemes for Interface Problems with Discontinuous Coefficients
- Convergence of Finite Volume Schemes for Poisson’s Equation on Nonuniform Meshes
- 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
- A Fast Iterative Algorithm for Elliptic Interface Problems
- Convergence of the ghost fluid method for elliptic equations with interfaces
- A finite element method for crack growth without remeshing
- Fast High Order Accurate Solution of Laplace’s Equation on Irregular Regions
- The Fast Solution of Poisson’s and the Biharmonic Equations on Irregular Regions
- The Immersed Interface Method
- Asymptotic adaptive methods for multi-scale problems in fluid mechanics