5 papers
An Immersed Interface Method for Parabolic Interface Problems with Nonlinear Jump Conditions
So-Hsiang Chou, Patrick Nyadjo Fonga
We develop an immersed interface finite difference method for a one-dimensional nonlinear parabolic interface problem with jump condition \[ [u]_α=λu^+u^-. \] The method combines a…
Second-Order Accuracy from Large Local Errors in Interface Problems: A Discrete Green's Function Analysis
So-Hsiang Chou, Patrick Nyadjo Fonga
Finite difference methods for interface problems often exhibit large local truncation errors near the interface, particularly when discontinuities in coefficients or solution deriv…
Raviart--Thomas Elements with Geometric Correction for Distorted Quadrilateral Meshes
So-Hsiang Chou
Mixed finite element methods based on Raviart--Thomas spaces are widely used for the numerical approximation of second--order elliptic problems in flux form. On quadrilateral meshe…
A Trace-Based Interface Reduction Method for Highly Conducting Interfaces
So-Hsiang Chou, Do Young Kwak
We develop a reduced interface formulation for elliptic interface problems with highly conducting interfaces. The interface condition consists of continuity of the primal variable…
A scalar interface reduction for nonlinear interface problems
So-Hsiang Chou
We study finite element approximations of elliptic and parabolic interface problems with discontinuous coefficients and nonlinear jump conditions. We introduce a scalar interface r…