Solutions to partial differential equations can exhibit singularities near non-smooth points of a domain, even when the given data is smooth. Depending on the geometry of the domain, corner singularities are among the most common singularities in practice, and have been a significant focus of research in the computational community. In this talk, we examine the prevalence of these singularities in mathematical modeling and demonstrate effective techniques to mitigate their impact in scientific computation, including the characterization of corner singularities, graded mesh algorithms, and mixed methods for high-order problems.

Contact: Robert Krasny.