The main focus of my research is adaptive, high-order, parallel methods for solution of partial differential equations.
N. Chalmers, L. Krivodonova, and R. Qin. Relaxing the CFL condition of the discontinuous Galerkin method, SIAM Journal on Scientific Computing, Vol. 36 (4), A2047-A2075, 2014.
J. Resch, L. Krivodonova and J. Vanderkooy. A Two-Dimensional Study of Finite Amplitude Sound Waves in a Trumpet Using the Discontinuous Galerkin Method, Journal of Computational Accoustics, Vol. 22(3), 2014.
D. Connor and L. Krivodonova. Interpolation of two-dimensional curves with Euler spirals, Journal of Applied and Computational Mathematics, Vol 261: 320-332, 2014.
L. Krivodonova and R. Qin. An analysis of the spectrum of the discontinuous Galerkin method II: Nonuniform grids , Applied Numerical Mathematics, Vol 71: 41-62, 2013.
L. Krivodonova and R. Qin. An analysis of the spectrum of the discontinuous Galerkin method, Applied Numerical Mathematics, Vol. 64:1-18, 2013.
R. Qin and L. Krivodonova. A discontinuous Galerkin method for solutions of the Euler equations on Cartesian grids with embedded geometries , Journal of Computational Science, Vol. 4 (1-2), 24-35, 2013.
L. Krivodonova. An Efficient Local Time Stepping Scheme for Solution of Nonlinear Conservation Laws. J. of Comp. Physics, Vol. 229:8537-8551, 2010.
L. Krivodonova. Limiters for High-Order Discontinuous Galerkin Methods. J. of Comp. Physics, Vol. 226(1):276-296,2007.
L. Krivodonova and M. Berger. High-order Accurate Implementation of Solid Wall Boundary Conditions in Curved Geometries. J. of Comp. Physics, Vol. 211:492-512, 2006.
L. Krivodonova, J. Xin, J.-F. Remacle, N. Chevaugeon, and J.E. Flaherty. Shock Detection and Limiting with Discontinuous Galerkin Methods for Hyperbolic Conservation Laws. Applied Numerical Mathematics, Vol. 48:323-338, 2004.
L. Krivodonova and J. Flaherty. Error Estimation for Discontinuous Galerkin Solutions of Multidimensional Hyperbolic Problems. Advances in Computational Mathematics, Vol. 19:57-71, 2003.
J. Flaherty, L. Krivodonova, J.-F. Remacle, and M. Shephard. Aspects of Discontinuous Galerkin Methods for Hyperbolic Conservation Laws. Finite Elements in Analysis and Design, Vol. 38:889 - 908, 2002.
S. Adjerid, K. Devine, J. Flaherty, and L. Krivodonova. A Posteriori Error
Estimation for Discontinuous Galerkin Solutions of Hyperbolic Problems.
Computer Methods in Applied Mechanics and Engineering, Vol. 191:1097-1112, 2002.