Contact details
Dr. Tatiana Shingel
Department of Mathematics
University of California, San Diego
9500 Gilman Drive, La Jolla, CA 92093-0112, USA
Office: APM 5747
Phone: +1(858)534-4889
Email: tshingel[at]math.ucsd.edu
Research Interests
- Nonlinear Approximation Theory
- Geometric Integration
- Computational Geometric Mechanics
- Multiscale Methods in Scientific Computing
Research Summary
My research is on approximation theory in manifolds with the view towards structure-preserving numerical integration methods for dynamical systems. Approximation in manifolds is a subfield of structured approximation, which is concerned with constructing lower-dimensional approximants of functions, while retaining the topological, geometric, or algebraic properties of the original function. Incorporating qualitative and geometric features into numerical methods for differential equations leads to significantly more accurate and efficient discretization algorithms. Approximation theory provides tools for numerical simulation of mathematical models described by differential equations. Given the amplifying recognition of geometric integration methods, there is a distinctive need to revitalize the complementary and synergistic relationship between numerical analysis and approximation theory, by developing a geometric approximation theory.