Accurate Solution and Gradient Computation for Elliptic Interface Problems with Variable Coefficients

DOI10.1137/15M1040244zbMath1362.76037WikidataQ42284183 ScholiaQ42284183MaRDI QIDQ5347511

Zhilin Li, Haifeng Ji, Xiaohong Chen

Publication date: 24 May 2017

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

zbMATH Keywords

interfaceM-matrixconvergence proofelliptic interface problemdiscrete Green functionaccurate gradient computationvariable coefficient with discontinuity

Mathematics Subject Classification ID

Finite difference methods applied to problems in fluid mechanics (76M20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Fictitious domain methods for initial value and initial-boundary value problems involving PDEs (65M85)

Related Items (26)

Enriched gradient recovery for interface solutions of the Poisson-Boltzmann equation ⋮ An ADI-Yee's scheme for Maxwell's equations with discontinuous coefficients ⋮ An augmented immersed finite element method for variable coefficient elliptic interface problems in two and three dimensions ⋮ New immersed finite volume element method for elliptic interface problems with non-homogeneous jump conditions ⋮ A direct IIM approach for two-phase Stokes equations with discontinuous viscosity on staggered grids ⋮ The immersed interface method for Helmholtz equations with degenerate diffusion ⋮ A condensed generalized finite element method (CGFEM) for interface problems ⋮ Nonconforming spectral element method: a friendly introduction in one dimension and a short review in higher dimensions ⋮ Kernel-free boundary integral method for two-phase Stokes equations with discontinuous viscosity on staggered grids ⋮ Sharp error estimates of a fourth‐order compact scheme for a Poisson interface problem ⋮ An augmented method for 4th order PDEs with discontinuous coefficients ⋮ Second order convergence of a modified MAC scheme for Stokes interface problems ⋮ Gradient recovery for elliptic interface problem. II: Immersed finite element methods ⋮ A simple augmented IIM for 3D incompressible two-phase Stokes flows with interfaces and singular forces ⋮ A new Petrov-Galerkin immersed finite element method for elliptic interface problems with non-homogeneous jump conditions ⋮ Gradient recovery for elliptic interface problem. III: Nitsche's method ⋮ Error estimates for an augmented method for one-dimensional elliptic interface problems ⋮ On MultiScale ADI Methods for Parabolic PDEs with a Discontinuous Coefficient ⋮ How to obtain an accurate gradient for interface problems? ⋮ A direct method for accurate solution and gradient computations for elliptic interface problems ⋮ Bilinear immersed finite volume element method for solving matrix coefficient elliptic interface problems with non-homogeneous jump conditions ⋮ A high order compact FD framework for elliptic BVPs involving singular sources, interfaces, and irregular domains ⋮ A multigrid based finite difference method for solving parabolic interface problem ⋮ On preconditioning the treecode-accelerated boundary integral (TABI) Poisson-Boltzmann solver ⋮ Stable generalized finite element method (SGFEM) for parabolic interface problems ⋮ A second-order boundary condition capturing method for solving the elliptic interface problems on irregular domains

Uses Software

• IIMPACK

Cites Work

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