AIMS Home

Recent Advancements in the Numerical Analysis of Nonlinear Partial Differential Equations

Organizer(s):
Name:	Affiliation:	Country:
Tom Lewis	University of North Carolina, Greensboro	USA
Yi Zhang	University of North Carolina, Greensboro	USA

Abstract:

This special session will highlight and address some of the current challenges for solving nonlinear partial differential equations (PDEs) numerically. PDEs have wide-ranging applications, and numerical methods remain an important tool for the understanding of solutions to PDEs. The emphasis in this session will be on theoretical results and computational results for reliably approximating solutions to nonlinear problems that are at the forefront of numerical PDEs; in particular, the rigorous study of convergence, admissibility, accuracy, and/or stability results or the formulation of highly efficient implementations and/or highly accurate methods for approximating application problems.

List of approved abstract
Name	Affiliation	Title
Shalmali Bandyopadhyay	University of North Carolina at Greensboro	Numerical Analysis of weak solutions for coupled elliptic systems with nonlinearity on the boundary
Satyajith B Boyana	University of North Caroliina, Greensboro	Dual-Wind Discontinuous Galerkin Method and its application to an Optimal Control Problem and a Parabolic Variational Inequality
Olena Burkovska	Oak Ridge National Laboratory	Nonlocal variational inequalities for phase-field modeling in solidification
Yanlai Chen	UMass Dartmouth	A new conservative discontinuous Galerkin method via implicit penalization for the generalized KdV equation
Christopher B Davis	Tennessee Tech	A Conforming Partition of Unity Method for a Class of Variational Inequalities of the Second Kind
Amanda E Diegel	Mississippi State University	Continuous Data Assimilation and Long-time Accuracy in a C0-IP Method for the Cahn-Hilliard Equation
Daniel X Guo	UNCW	Numerical solutions of the Nonlinear Korteweg-de Vries equation
Xingjie Li	University of North Carolina Charlotte	ISALT: Inference-based schemes adaptive to large time-stepping for locally Lipschitz ergodic systems
Nana Adjoah Mbroh	North-West University	A second order fitted operator finite difference scheme for a modified Burgers equation
Quinn A Morris	Appalachian State University	Numerical methods for approximating sublinear positone and semipositone boundary value problems using finite difference methods
Aaron Rapp	University of the Virgin Islands	Approximating the solutions to Hamilton-Jacobi equations with dual-wind discontinuous Galerkin methods.
Stefan Schnake	Oak Ridge National Laboratory	A Predictor-Corrector Strategy for Adaptivity in Dynamical Low-Rank Approximations
Xiaochuan Tian	University of California, San Diego	A convergent monotone scheme for a nonlocal segregation model with free boundary
Axel Turnquist	University of Texas at Austin	Finite-Difference Methods for Computing Optimal Transport PDE on the Unit Sphere
Liet Vo	University of Illinois Chicago	Higher order time discretization method for a class of semilinear stochastic PDEs with multiplicative noise
Xiaohuan Xue	University of North Carolina at Greensboro	Convergent Finite Difference Methods with Higher Order Local Truncation Errors for Stationary Hamilton-Jacobi Equations
Qihao Ye	University of California San Diego (UCSD)	Monotone meshfree methods for linear elliptic equations in non-divergence form via nonlocal relaxation
Jia Zhao	Utah State University	A general framework to derive linear, decoupled and energy-stable schemes for reversible-irreversible thermodynamically consistent models