1 citations · 1 across the 10 of their papers we have counts for
11 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…
A Lifting-Based Interface Reduction Framework for Nonlinear Transmission and Eigenvalue Problems
So-Hsiang Chou
We present a lifting-based interface reduction framework for nonlinear transmission and eigenvalue problems. The method represents the solution as a sum of a bulk component and a l…
Interface Reduction for Elliptic Interface Problems with Conservative Flux Reconstruction
C. Attanayake, So-Hsiang Chou
We propose a low-dimensional interface reduction method for elliptic interface problems based on conservative flux reconstruction. The approach combines a fitted finite eleme…
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…
High-Order Enriched Finite Element Methods for Elliptic Interface Problems with Discontinuous Solutions
Champike Attanayake, So-Hsiang Chou, Quanling Deng
Elliptic interface problems whose solutions are continuous have been well studied over the past two decades. The well-known numerical methods include the strongly stable gene…
Flux Recovery and Superconvergence of Quadratic Immersed Interface Finite Elements
So-Hsiang Chou, C. Attanayake
We introduce a flux recovery scheme for the computed solution of a quadratic immersed finite element method. The recovery is done at nodes and interface point first and by interpol…
Optimal Order Convergence Implies Numerical Smoothness
So-Hsiang Chou
It is natural to expect the following loosely stated approximation principle to hold: a numerical approximation solution should be in some sense as smooth as its target exact solut…