[1] Asthana, K., López-Morales, M.R., Jameson, A.: Non-linear stabilization of high-order flux reconstruction schemes via Fourier-spectral filtering. J. Comput. Phys. 303, 269–294 (2015)
[2] Bohm, M., Schermeng, S., Winters, A.R., Gassner, G.J., Jacobs, G.B.: Multi-element SIAC filter for shock capturing applied to high-order discontinuous Galerkin spectral element methods. J. Sci. Comput. 81(2), 820–844 (2019)
[3] Bramble, J.H., Schatz, A.H.: Higher order local accuracy by averaging in the finite element method. Math. Comput. 31(137), 94–111 (1977)
[4] Cockburn, B., Hou, S., Shu, C.-W.: The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV. The multidimensional case. Math. Comput. 54(190), 545–581 (1990)
[5] Cockburn, B., Lin, S.Y., Shu, C.-W.: TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III. One-dimensional systems. J. Comput. Phys. 84(1), 90–113 (1989)
[6] Cockburn, B., Luskin, M., Shu, C.-W., Süli, E.: Enhanced accuracy by post-processing for finite element methods for hyperbolic equations. Math. Comput. 72(242), 577–606 (2003)
[7] Cockburn, B., Shu, C.-W.: TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. II. General framework. Math. Comput. 52(186), 411–435 (1989)
[8] Cockburn, B., Shu, C.-W.: The Runge-Kutta local projection \begin{document}$ P^1 $\end{document}-discontinuous-Galerkin finite element method for scalar conservation laws. RAIRO Modél. Math. Anal. Numér. 25(3), 337–361 (1991)
[9] Curtis, S., Kirby, R.M., Ryan, J.K., Shu, C.-W.: Postprocessing for the discontinuous Galerkin method over nonuniform meshes. SIAM J. Sci. Comput. 30(1), 272–289 (2007)
[10] Docampo-Sánchez, J., Jacobs, G.B., Li, X., Ryan, J.K.: Enhancing accuracy with a convolution filter: what works and why!. Comput. Fluids 213, 104727 (2020)
[11] Docampo-Sánchez, J., Ryan, J.K., Mirzargar, M., Kirby, R.M.: Multi-dimensional filtering: reducing the dimension through rotation. SIAM J. Sci. Comput. 39(5), A2179–A2200 (2017)
[12] Edoh, A.K., Mundis, N.L., Merkle, C.L., Karagozian, A.R., Sankaran, V.: Comparison of artificial-dissipation and solution-filtering stabilization schemes for time-accurate simulations. J. Comput. Phys. 375, 1424–1450 (2018)
[13] Jallepalli, A., Docampo-Sanchez, J., Ryan, J.K., Haimes, R., Kirby, R.M.: On the treatment of field quantities and elemental continuity in fem solutions. IEEE Trans. Vis. Comput. Graph. 24(1), 903–912 (2018)
[14] Jallepalli, A., Haimes, R., Kirby, R.M.: Adaptive characteristic length for L-SIAC filtering of FEM data. J. Sci. Comput. 79(1), 542–563 (2019)
[15] Ji, L., Ryan, J.K.: Smoothness-increasing accuracy-conserving (SIAC) filters in Fourier space. In: Spectral and High Order Methods for Partial Differential Equations—ICOSAHOM 2014, Lecture Notes in Computational Science and Engineering, vol. 106, pp. 415–423. Springer, Cham (2015)
[16] King, J., Mirzaee, H., Ryan, J.K., Kirby, R.M.: Smoothness-increasing accuracy-conserving (SIAC) filtering for discontinuous Galerkin solutions: improved errors versus higher-order accuracy. J. Sci. Comput. 53(1), 129–149 (2012)
[17] Li, X., Ryan, J.K.: SIAC filtering for nonlinear hyperbolic equations. In: Interdisciplinary Topics in Applied Mathematics. Modeling and Computational Science, pp. 285–291. Springer International Publishing, Cham (2015)
[18] Li, X., Ryan, J.K., Kirby, R.M., Vuik, C.: Smoothness-increasing accuracy-conserving (SIAC) filters for derivative approximations of discontinuous Galerkin (DG) solutions over nonuniform meshes and near boundaries. J. Comput. Appl. Math. 294, 275–296 (2016)
[19] Li, X., Ryan, J.K., Kirby, R.M., Vuik, K.: Smoothness-increasing accuracy-conserving (SIAC) filtering for discontinuous Galerkin solutions over nonuniform meshes: superconvergence and optimal accuracy. J. Sci. Comput. 81(3), 1150–1180 (2019)
[20] Mirzaee, H., Ryan, J.K., Kirby, R.M.: Quantification of errors introduced in the numerical approximation and implementation of smoothness-increasing accuracy conserving (SIAC) filtering of discontinuous Galerkin (DG) fields. J. Sci. Comput. 45(1/2/3), 447–470 (2010)
[21] Mirzaee, H., Ryan, J.K., Kirby, R.M.: Efficient implementation of smoothness-increasing accuracy-conserving (SIAC) filters for discontinuous Galerkin solutions. J. Sci. Comput. 52(1), 85–112 (2012)
[22] Mirzargar, M., Jallepalli, A., Ryan, J.K., Kirby, R.M.: Hexagonal smoothness-increasing accuracy-conserving filtering. J. Sci. Comput. 73(2/3), 1072–1093 (2017)
[23] Reed, W., Hill, T.: Triangular mesh methods for the neutron transport equation. Los Alamos Report LA-UR-73-479. Los Alamos Scientific Laboratory, Los Alamos, NM (1973)
[24] Ryan, J.K., Cockburn, B.: Local derivative post-processing for the discontinuous Galerkin method. J. Comput. Phys. 228(23), 8642–8664 (2009)
[25] Ryan, J.K., Docampo-Sanchez, J.: One-dimensional line SIAC filtering for multi-dimensions: applications to streamline visualization. In: van Brummelen, H., Corsini, A., Perotto, S., Rozza, G. (eds) Numerical Methods for Flows: FEF 2017 Selected Contributions, pp. 145–154. Springer International Publishing, Cham (2020)
[26] Ryan, J.K., Li, X., Kirby, R.M., Vuik, K.: One-sided position-dependent smoothness-increasing accuracy-conserving (SIAC) filtering over uniform and non-uniform meshes. J. Sci. Comput. 64(3), 773–817 (2015)
[27] Ryan, J.K., Shu, C.-W., Atkins, H.: Extension of a postprocessing technique for the discontinuous Galerkin method for hyperbolic equations with application to an aeroacoustic problem. SIAM J. Sci. Comput. 26(3), 821–843 (2005)
[28] Van Slingerland, P., Ryan, J.K., Vuik, C.: Position-dependent smoothness-increasing accuracy-conserving (SIAC) filtering for improving discontinuous Galerkin solutions. SIAM J. Sci. Comput. 33(2), 802–825 (2011)
[29] Steffen, M., Curtis, S., Kirby, R.M., Ryan, J.K.: Investigation of smoothness-increasing accuracy-conserving filters for improving streamline integration through discontinuous fields. Vis. Comput. Graph. IEEE Trans. 14(3), 680–692 (2008)
[30] Vandeven, H.: Family of spectral filters for discontinuous problems. J. Sci. Comput. 6(2), 159–192 (1991)
[31] Walfisch, D., Ryan, J.K., Kirby, R.M., Haimes, R.: One-sided smoothness-increasing accuracy-conserving filtering for enhanced streamline integration through discontinuous fields. J. Sci. Comput. 38(2), 164–184 (2009)
[32] Wissink, B.W., Jacobs, G.B., Ryan, J.K., Don, W.S., van der Weide, E.T.A.: Shock regularization with smoothness-increasing accuracy-conserving Dirac-delta polynomial kernels. J. Sci. Comput. 77(1), 579–596 (2018)
[33] Zhang, Z., Naga, A.: A new finite element gradient recovery method: superconvergence property. SIAM J. Sci. Comput. 26(4), 1192–1213 (2005)
[34] Zhang, Z., Zhu, J.: Analysis of the superconvergent patch recovery technique and a posteriori error estimator in the finite element method. I. Comput. Methods Appl. Mech. Eng. 123(1/2/3/4), 173–187 (1995)
[35] Zhang, Z., Zhu, J.Z.: Analysis of the superconvergent patch recovery technique and a posteriori error estimator in the finite element method. II. Comput. Methods Appl. Mech. Eng. 163(1/2/3/4), 159–170 (1998)
