4 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…
Construction of Discontinuous Enrichment Functions for Enriched FEM's for Interface Elliptic Problems in 1D
So-Hsiang Chou, Champike Attanayake
We introduce an enriched unfitted finite element method to solve 1D elliptic interface problems with discontinuous solutions, including those having implicit or Robin-type interfac…