Improved volume conservation in the computation of flows with immersed elastic boundaries
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A Fast Iterative Algorithm for Elliptic Interface Problems
SIAM Journal on Numerical Analysis
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
A boundary condition capturing method for Poisson's equation on irregular domains
Journal of Computational Physics
A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
Journal of Computational Physics
Convergence of the ghost fluid method for elliptic equations with interfaces
Mathematics of Computation
A Boundary Condition--Capturing Multigrid Approach to Irregular Boundary Problems
SIAM Journal on Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces
Journal of Computational Physics
Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities
Journal of Computational Physics
A kernel-free boundary integral method for elliptic boundary value problems
Journal of Computational Physics
Piecewise-polynomial discretization and Krylov-accelerated multigrid for elliptic interface problems
Journal of Computational Physics
A sharp interface finite volume method for elliptic equations on Cartesian grids
Journal of Computational Physics
An interpolation matched interface and boundary method for elliptic interface problems
Journal of Computational and Applied Mathematics
A second order virtual node method for elliptic problems with interfaces and irregular domains
Journal of Computational Physics
Numerical method for solving matrix coefficient elliptic equation with sharp-edged interfaces
Journal of Computational Physics
MIB method for elliptic equations with multi-material interfaces
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
An Analysis of a Broken $P_1$-Nonconforming Finite Element Method for Interface Problems
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
A weak formulation for solving elliptic interface problems without body fitted grid
Journal of Computational Physics
An asymptotic solution approach for elliptic equations with discontinuous coefficients
Journal of Computational Physics
Hi-index | 31.54 |
A new 2nd order accurate numerical method on non-body-fitting grids is proposed for solving the variable coefficient elliptic equation in disjoint subdomains @W^+/- separated by interfaces @C. The variable coefficients, the source term, and hence the solution itself and its derivatives may be discontinuous across the interfaces. Jump conditions in solution and its co-normal derivative at interface are prescribed. Instead of smooth, the interfaces are only required to be Lipschitz continuous as submanifold. A weak formulation is developed, the existence, uniqueness and regularity of the solutions are studied. The numerical method is derived by discretizing the weak formulation. The method is different from traditional finite element methods. Extensive numerical experiments are presented and show that the method is 2nd order accurate in solution and 1st order accurate in its gradient in L^~ norm if the interface is C^2 and solutions are C^2 on the closures of the subdomains. The method can handle the problems when the solutions and/or the interfaces are weaker than C^2. For example, u@?H^2(@W^+/-), @C is Lipschitz continuous and their singularities coincide, see Example 18 in Section 4. The accuracies of the method under various circumstances are listed in Table 19.