Research at FAST

91 Department of Applied Mathematics Department of Applied Mathematics Qualification PhD (CityU) Postdoc (CityU) ORCID ID 0000-0001-7566-3464 Dr LI Buyang Associate Professor Research Overview Numerical methods for PDEs, stability and convergence of numerical solutions, including • PDEs on surfaces, surface evolution, mean curvature flow • Strongly nonlinear gradient flow • Maximal L p -regularity of time discretization methods for parabolic equations • Analyticity, maximum-norm stability, and maximal L p -regularity of finite element solutions to parabolic equations • Artificial boundary conditions/boundary integral equations for wave propagation in an unbounded domain • Optimal control of parabolic and wave equations • High-order approximation of fractional evolution equations • Dynamic Ginzburg-Landau superconductivity equations • Thermistors with sensitive temperature-dependent electric conductivity • Modelling and computation of sweat transport in porous textile materials Well-posedness of nonlinear PDEs • Time-dependent Joule heating problem (for thermistors with temperature-dependent electric conductivity) • Heat and moisture transport in fibrous media Representative Publications • B. Kovács, B. Li , and C. Lubich: A convergent evolving finite element algorithm for mean curvature flow of closed surfaces. Numer. Math. 143 ( 2019 ), pp. 797-853 • B. Li : Analyticity, maximal regularity and maximum- norm stability of semi-discrete finite element solutions of parabolic equations in nonconvex polyhedra. Math. Comp. 88 ( 2019 ), pp. 1-44 • B. Li and Z. Zhang: Mathematical and numerical analysis of time-dependent Ginzburg-Landau equations in nonconvex polygons based on Hodge decomposition. Math. Comp. 86 ( 2017 ), pp. 1579-1608 • B . Ková c s , B . L i and C. Lub i ch: A - s t ab l e t ime discretizations preserve maximal parabolic regularity. SIAM J. Numer. Anal. 54 ( 2016 ), pp. 3600-3624 • B. Li and W. Sun: Unconditional convergence and optimal error estimates of a Galerkin-mixed FEM for incompressible miscible flow in porous media. SIAM J. Numer. Anal. 51 ( 2013 ), pp. 1959-1977 Evolving surface under mean curvature flow (formation of singularity)