Antonio Baeza

Analysis of WENO Schemes for Full and Global Accuracy

Liu, Osher, and Chan introduced weighted essentially nonoscillatory (WENO) reconstructions in [X.-D. Liu, S. Osher, and T. Chan, J. Comput. Phys., 115 (1994), pp. 200-212] to improve the order of accuracy of essentially nonoscillatory (ENO) reconstructions [A. Harten et al., J. Comput. Phys., 71 (1987), pp. 231-303]. In [G.-S. Jiang and C.-W. Shu, J. Comput. Phys., 126 (1996), pp. 202-228], the authors proposed smoothness indicators to obtain a WENO fifth order reconstruction from third order ENO reconstructions. With these smoothness indicators, Balsara and Shu [J. Comput. Phys., 160 (2000), pp. 405-452] and, later, [G. A. Gerolymos, D. Senechal, and I. Vallet, J. Comput. Phys., 228 (2009), pp. 8481-8524] obtained

Discrete multiresolution based on hermite interpolation: computing derivatives

(2r-1)

High Order Boundary Extrapolation Technique for Finite Difference Methods on Complex Domains with Cartesian Meshes

th order WENO reconstructions from

An Approximate Lax---Wendroff-Type Procedure for High Order Accurate Schemes for Hyperbolic Conservation Laws

r

High Order Weighted Extrapolation for Boundary Conditions for Finite Difference Methods on Complex Domains with Cartesian Meshes

th order ENO reconstructions for

A new class of non-linear monotone Hermite interpolants

4\leq r\leq 6

Vector cell-average multiresolution based on Hermite interpolation

, resp.,

Highly Accurate Conservative Finite Difference Schemes and Adaptive Mesh Refinement Techniques for Hyperbolic Systems of Conservation Laws

7\leq r\leq 9

Central WENO Schemes Through a Global Average Weight

. In [A. K. Henrick, T. D. Aslam, and J. M. Powers, J. Comput. Phys., 207 (2005), pp. 542-567], the authors noticed that these reconstructions do not attain the optimal order

High Order in Space and Time Schemes Through an Approximate Lax-Wendroff Procedure

2r-1