Special Session 79: Recent Advancements in the Numerical Analysis of Nonlinear Partial Differential Equations
Organizer(s): Tom Lewis , Yi Zhang

Parallel Session 9 :: Saturday, June 3, 08:00 – 09:30                     ST1005
8:00-8:30	Liet Vo (University of Illinois Chicago, USA)  Higher order time discretization method for a class of semilinear stochastic PDEs with multiplicative noise

8:30-9:00

Aaron Rapp (University of the Virgin Islands, USA)  Approximating the solutions to Hamilton-Jacobi equations with dual-wind discontinuous Galerkin methods.

9:00-9:30

Stefan Schnake (Oak Ridge National Laboratory, USA)  A Predictor-Corrector Strategy for Adaptivity in Dynamical Low-Rank Approximations

Parallel Session 10 :: Saturday, June 3, 14:00 – 16:00                     ST1005
14:00-14:30	Amanda E Diegel (Mississippi State University, USA)  Continuous Data Assimilation and Long-time Accuracy in a C0-IP Method for the Cahn-Hilliard Equation

14:30-15:00

Satyajith B Boyana (University of North Caroliina, Greensboro, USA)  Dual-Wind Discontinuous Galerkin Method and its application to an Optimal Control Problem and a Parabolic Variational Inequality

15:00-15:30

Christopher B Davis (Tennessee Tech, USA)  A Conforming Partition of Unity Method for a Class of Variational Inequalities of the Second Kind

15:30-16:00

Olena Burkovska (Oak Ridge National Laboratory, USA)  Nonlocal variational inequalities for phase-field modeling in solidification

Parallel Session 11 :: Saturday, June 3, 16:30 – 19:00                     ST1005
16:30-17:00	Daniel X Guo (UNCW, USA)  Numerical solutions of the Nonlinear Korteweg-de Vries equation

17:00-17:30

Yanlai Chen (UMass Dartmouth, USA)  A new conservative discontinuous Galerkin method via implicit penalization for the generalized KdV equation

17:30-18:00

Xingjie Li (University of North Carolina Charlotte, USA)  ISALT: Inference-based schemes adaptive to large time-stepping for locally Lipschitz ergodic systems

Parallel Session 12 :: Sunday, June 4, 08:00 – 10:00                     ST1005
8:30-9:00	Shalmali Bandyopadhyay (University of North Carolina at Greensboro, India)  Numerical Analysis of weak solutions for coupled elliptic systems with nonlinearity on the boundary

9:00-9:30

Quinn A Morris (Appalachian State University, USA)  Numerical methods for approximating sublinear positone and semipositone boundary value problems using finite difference methods

9:30-10:00

Xiaohuan Xue (University of North Carolina at Greensboro, USA)  Convergent Finite Difference Methods with Higher Order Local Truncation Errors for Stationary Hamilton-Jacobi Equations

Parallel Session 13 :: Sunday, June 4, 10:30 – 12:30                     ST1005
10:30-11:00	Qihao Ye (University of California San Diego (UCSD), USA)  Monotone meshfree methods for linear elliptic equations in non-divergence form via nonlocal relaxation

11:00-11:30

Xiaochuan Tian (University of California, San Diego, USA)  A convergent monotone scheme for a nonlocal segregation model with free boundary

11:30-12:00

Axel Turnquist (University of Texas at Austin, USA)  Finite-Difference Methods for Computing Optimal Transport PDE on the Unit Sphere

12:00-12:30

Nana Adjoah N Mbroh (North-West University, So Africa)  A second order fitted operator finite difference scheme for a modified Burgers equation