Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

A Collection of 2D Elliptic Problems for Testing Adaptive Algorithms



William F. Mitchell


Adaptive grid refinement is a critical component of the improvements that have recently been made in algorithms for the numerical solution of partial differential equations (PDEs). The development of new algorithms and computer codes for the solution of PDEs usually involves the use of proof-of-concept test problems. 2D elliptic problems are often used as the first test bed for new algorithms and codes. This paper contains a set of twelve parametrized 2D elliptic test problems for adaptive grid refinement algorithms and codes. The problems exhibit a variety of types of singularities, near singularities, and other difficulties.
NIST Interagency/Internal Report (NISTIR) - 7668
Report Number


adaptive grid refinement, elliptic partial differential equations, test problems


Mitchell, W. (2010), A Collection of 2D Elliptic Problems for Testing Adaptive Algorithms, NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed February 24, 2024)
Created February 26, 2010, Updated June 2, 2021