Chen, Chen; Dawson, Clint; Valseth, Eirik Cross-mode stabilized stochastic shallow water systems using stochastic finite element methods. (English) Zbl 07653073 Comput. Methods Appl. Mech. Eng. 405, Article ID 115873, 51 p. (2023). MSC: 65M60 35Q35 35R60 PDFBibTeX XMLCite \textit{C. Chen} et al., Comput. Methods Appl. Mech. Eng. 405, Article ID 115873, 51 p. (2023; Zbl 07653073) Full Text: DOI arXiv
Bremer, Maximilian; Bachan, John; Chan, Cy; Dawson, Clint Adaptive total variation stable local timestepping for conservation laws. (English) Zbl 07536744 J. Comput. Phys. 463, Article ID 111176, 25 p. (2022). MSC: 65Mxx 76Mxx 35Lxx PDFBibTeX XMLCite \textit{M. Bremer} et al., J. Comput. Phys. 463, Article ID 111176, 25 p. (2022; Zbl 07536744) Full Text: DOI arXiv
Valseth, Eirik; Dawson, Clint A stable space-time FE method for the shallow water equations. (English) Zbl 1484.76045 Comput. Geosci. 26, No. 1, 53-70 (2022). MSC: 76M10 65M60 PDFBibTeX XMLCite \textit{E. Valseth} and \textit{C. Dawson}, Comput. Geosci. 26, No. 1, 53--70 (2022; Zbl 1484.76045) Full Text: DOI arXiv
Kazhyken, Kazbek; Videman, Juha; Dawson, Clint Discontinuous Galerkin methods for a dispersive wave hydro-morphodynamic model with bed-load transport. (English) Zbl 1506.76087 Comput. Methods Appl. Mech. Eng. 375, Article ID 113592, 20 p. (2021). MSC: 76M10 65M60 76B15 PDFBibTeX XMLCite \textit{K. Kazhyken} et al., Comput. Methods Appl. Mech. Eng. 375, Article ID 113592, 20 p. (2021; Zbl 1506.76087) Full Text: DOI arXiv
Brus, S. R.; Wirasaet, D.; Kubatko, E. J.; Westerink, J. J.; Dawson, C. High-order discontinuous Galerkin methods for coastal hydrodynamics applications. (English) Zbl 1441.76054 Comput. Methods Appl. Mech. Eng. 355, 860-899 (2019). MSC: 76M10 65M60 76B15 76D33 86A05 PDFBibTeX XMLCite \textit{S. R. Brus} et al., Comput. Methods Appl. Mech. Eng. 355, 860--899 (2019; Zbl 1441.76054) Full Text: DOI
Samii, Ali; Kazhyken, Kazbek; Michoski, Craig; Dawson, Clint A comparison of the explicit and implicit hybridizable discontinuous Galerkin methods for nonlinear shallow water equations. (English) Zbl 1428.65093 J. Sci. Comput. 80, No. 3, 1936-1956 (2019). MSC: 65N30 65L06 35Q35 76B15 76M10 PDFBibTeX XMLCite \textit{A. Samii} et al., J. Sci. Comput. 80, No. 3, 1936--1956 (2019; Zbl 1428.65093) Full Text: DOI
Bremer, Maximilian; Kazhyken, Kazbek; Kaiser, Hartmut; Michoski, Craig; Dawson, Clint Performance comparison of HPX versus traditional parallelization strategies for the discontinuous Galerkin method. (English) Zbl 1427.65238 J. Sci. Comput. 80, No. 2, 878-902 (2019). MSC: 65M60 65Y10 76B15 76M10 PDFBibTeX XMLCite \textit{M. Bremer} et al., J. Sci. Comput. 80, No. 2, 878--902 (2019; Zbl 1427.65238) Full Text: DOI
Trahan, C. J.; Savant, G.; Berger, R. C.; Farthing, M.; McAlpin, T. O.; Pettey, L.; Choudhary, G. K.; Dawson, C. N. Formulation and application of the adaptive hydraulics three-dimensional shallow water and transport models. (English) Zbl 1416.76130 J. Comput. Phys. 374, 47-90 (2018). MSC: 76M10 86A05 76B15 86-08 PDFBibTeX XMLCite \textit{C. J. Trahan} et al., J. Comput. Phys. 374, 47--90 (2018; Zbl 1416.76130) Full Text: DOI
Giraldi, Loïc; Le Maître, Olivier P.; Mandli, Kyle T.; Dawson, Clint N.; Hoteit, Ibrahim; Knio, Omar M. Bayesian inference of earthquake parameters from buoy data using a polynomial chaos-based surrogate. (English) Zbl 1369.86007 Comput. Geosci. 21, No. 4, 683-699 (2017). MSC: 86A15 62P12 62F15 PDFBibTeX XMLCite \textit{L. Giraldi} et al., Comput. Geosci. 21, No. 4, 683--699 (2017; Zbl 1369.86007) Full Text: DOI
Brus, S. R.; Wirasaet, D.; Westerink, J. J.; Dawson, C. Performance and scalability improvements for discontinuous Galerkin solutions to conservation laws on unstructured grids. (English) Zbl 1359.65195 J. Sci. Comput. 70, No. 1, 210-242 (2017). MSC: 65M60 65Y05 65Y20 35L65 76D05 76B15 76M10 PDFBibTeX XMLCite \textit{S. R. Brus} et al., J. Sci. Comput. 70, No. 1, 210--242 (2017; Zbl 1359.65195) Full Text: DOI
Wirasaet, D.; Brus, S. R.; Michoski, C. E.; Kubatko, E. J.; Westerink, J. J.; Dawson, C. Artificial boundary layers in discontinuous Galerkin solutions to shallow water equations in channels. (English) Zbl 1351.76085 J. Comput. Phys. 299, 597-612 (2015). MSC: 76M10 65M60 35Q53 76B15 PDFBibTeX XMLCite \textit{D. Wirasaet} et al., J. Comput. Phys. 299, 597--612 (2015; Zbl 1351.76085) Full Text: DOI
Mirabito, Chris; Dawson, Clint; Aizinger, Vadym An a priori error estimate for the local discontinuous Galerkin method applied to two-dimensional shallow water and morphodynamic flow. (English) Zbl 1325.76120 Numer. Methods Partial Differ. Equations 31, No. 2, 397-421 (2015). MSC: 76M10 65M60 76B15 76T20 PDFBibTeX XMLCite \textit{C. Mirabito} et al., Numer. Methods Partial Differ. Equations 31, No. 2, 397--421 (2015; Zbl 1325.76120) Full Text: DOI
Meixner, Jessica; Dietrich, J. Casey; Dawson, Clint; Zijlema, Marcel; Holthuijsen, Leo H. A discontinuous Galerkin coupled wave propagation/circulation model. (English) Zbl 1299.76146 J. Sci. Comput. 59, No. 2, 334-370 (2014). MSC: 76M10 PDFBibTeX XMLCite \textit{J. Meixner} et al., J. Sci. Comput. 59, No. 2, 334--370 (2014; Zbl 1299.76146) Full Text: DOI
Wirasaet, D.; Kubatko, E. J.; Michoski, C. E.; Tanaka, S.; Westerink, J. J.; Dawson, C. Discontinuous Galerkin methods with nodal and hybrid modal/nodal triangular, quadrilateral, and polygonal elements for nonlinear shallow water flow. (English) Zbl 1296.76089 Comput. Methods Appl. Mech. Eng. 270, 113-149 (2014). MSC: 76M10 65M60 76B15 PDFBibTeX XMLCite \textit{D. Wirasaet} et al., Comput. Methods Appl. Mech. Eng. 270, 113--149 (2014; Zbl 1296.76089) Full Text: DOI
Dawson, Clint A local timestepping Runge-Kutta discontinuous Galerkin method for hurricane storm surge modeling. (English) Zbl 1280.86007 Feng, Xiaobing (ed.) et al., Recent developments in discontinuous Galerkin finite element methods for partial differential equations. Papers based on the 2012 John H. Barrett memorial lectures, Knoxville, TN, USA, May 9–11, 2012. Cham: Springer (ISBN 978-3-319-01817-1/hbk; 978-3-319-01818-8/ebook). The IMA Volumes in Mathematics and its Applications 157, 133-148 (2014). MSC: 86A10 86-08 65N30 PDFBibTeX XMLCite \textit{C. Dawson}, IMA Vol. Math. Appl. 157, 133--148 (2014; Zbl 1280.86007) Full Text: DOI
Dawson, Clint; Videman, Juha H. A streamline diffusion finite element method for the viscous shallow water equations. (English) Zbl 1288.65141 J. Comput. Appl. Math. 251, 1-7 (2013). MSC: 65M60 65M15 76M10 PDFBibTeX XMLCite \textit{C. Dawson} and \textit{J. H. Videman}, J. Comput. Appl. Math. 251, 1--7 (2013; Zbl 1288.65141) Full Text: DOI
Dawson, Clint; Trahan, Corey Jason; Kubatko, Ethan J.; Westerink, Joannes J. A parallel local timestepping Runge-Kutta discontinuous Galerkin method with applications to coastal Ocean modeling. (English) Zbl 1286.86008 Comput. Methods Appl. Mech. Eng. 259, 154-165 (2013). MSC: 86A05 86-08 76M10 65M60 76B15 PDFBibTeX XMLCite \textit{C. Dawson} et al., Comput. Methods Appl. Mech. Eng. 259, 154--165 (2013; Zbl 1286.86008) Full Text: DOI
Trahan, Corey J.; Dawson, Clint Local time-stepping in Runge-Kutta discontinuous Galerkin finite element methods applied to the shallow-water equations. (English) Zbl 1253.76065 Comput. Methods Appl. Mech. Eng. 217-220, 139-152 (2012). MSC: 76M10 76D05 65M60 PDFBibTeX XMLCite \textit{C. J. Trahan} and \textit{C. Dawson}, Comput. Methods Appl. Mech. Eng. 217--220, 139--152 (2012; Zbl 1253.76065) Full Text: DOI
Tanaka, S.; Bunya, S.; Westerink, J. J.; Dawson, C.; Luettich, R. A. jun. Scalability of an unstructured grid continuous Galerkin based hurricane storm surge model. (English) Zbl 1270.76038 J. Sci. Comput. 46, No. 3, 329-358 (2011). MSC: 76M10 76B15 76U05 86A05 PDFBibTeX XMLCite \textit{S. Tanaka} et al., J. Sci. Comput. 46, No. 3, 329--358 (2011; Zbl 1270.76038) Full Text: DOI Link
Santillana, Mauricio; Dawson, Clint A local discontinuous Galerkin method for a doubly nonlinear diffusion equation arising in shallow water modeling. (English) Zbl 1231.76163 Comput. Methods Appl. Mech. Eng. 199, No. 23-24, 1424-1436 (2010). MSC: 76M10 76R50 PDFBibTeX XMLCite \textit{M. Santillana} and \textit{C. Dawson}, Comput. Methods Appl. Mech. Eng. 199, No. 23--24, 1424--1436 (2010; Zbl 1231.76163) Full Text: DOI
Mirabito, C.; Dawson, C.; Kubatko, E. J.; Westerink, J. J.; Bunya, S. Implementation of a discontinuous Galerkin morphological model on two-dimensional unstructured meshes. (English) Zbl 1225.76201 Comput. Methods Appl. Mech. Eng. 200, No. 1-4, 189-207 (2011). MSC: 76M10 76B15 86A05 PDFBibTeX XMLCite \textit{C. Mirabito} et al., Comput. Methods Appl. Mech. Eng. 200, No. 1--4, 189--207 (2010; Zbl 1225.76201) Full Text: DOI
Santillana, Mauricio; Dawson, Clint A numerical approach to study the properties of solutions of the diffusive wave approximation of the shallow water equations. (English) Zbl 1398.76025 Comput. Geosci. 14, No. 1, 31-53 (2010). MSC: 76B15 76M10 65M60 PDFBibTeX XMLCite \textit{M. Santillana} and \textit{C. Dawson}, Comput. Geosci. 14, No. 1, 31--53 (2010; Zbl 1398.76025) Full Text: DOI
Kubatko, Ethan J.; Bunya, Shintaro; Dawson, Clint; Westerink, Joannes J. Dynamic \(p\)-adaptive Runge-Kutta discontinuous Galerkin methods for the shallow water equations. (English) Zbl 1227.76032 Comput. Methods Appl. Mech. Eng. 198, No. 21-26, 1766-1774 (2009). MSC: 76M10 76M20 76B10 86A05 PDFBibTeX XMLCite \textit{E. J. Kubatko} et al., Comput. Methods Appl. Mech. Eng. 198, No. 21--26, 1766--1774 (2009; Zbl 1227.76032) Full Text: DOI
Bunya, Shintaro; Kubatko, Ethan J.; Westerink, Joannes J.; Dawson, Clint A wetting and drying treatment for the Runge-Kutta discontinuous Galerkin solution to the shallow water equations. (English) Zbl 1227.76026 Comput. Methods Appl. Mech. Eng. 198, No. 17-20, 1548-1562 (2009). MSC: 76M10 76M20 76B10 PDFBibTeX XMLCite \textit{S. Bunya} et al., Comput. Methods Appl. Mech. Eng. 198, No. 17--20, 1548--1562 (2009; Zbl 1227.76026) Full Text: DOI
Kubatko, Ethan J.; Bunya, Shintaro; Dawson, Clint; Westerink, Joannes J.; Mirabito, Chris A performance comparison of continuous and discontinuous finite element shallow water models. (English) Zbl 1203.76085 J. Sci. Comput. 40, No. 1-3, 315-339 (2009). MSC: 76M10 65M60 65Y05 PDFBibTeX XMLCite \textit{E. J. Kubatko} et al., J. Sci. Comput. 40, No. 1--3, 315--339 (2009; Zbl 1203.76085) Full Text: DOI Link
Dawson, Clint A continuous/discontinuous Galerkin framework for modeling coupled subsurface and surface water flow. (English) Zbl 1259.86001 Comput. Geosci. 12, No. 4, 451-472 (2008). MSC: 86-08 86A05 76M10 76S05 65M60 PDFBibTeX XMLCite \textit{C. Dawson}, Comput. Geosci. 12, No. 4, 451--472 (2008; Zbl 1259.86001) Full Text: DOI
Alonso, R.; Santillana, M.; Dawson, C. On the diffusive wave approximation of the shallow water equations. (English) Zbl 1154.35428 Eur. J. Appl. Math. 19, No. 5, 575-606 (2008). MSC: 35Q35 76B15 76B03 35A35 35B05 35B65 PDFBibTeX XMLCite \textit{R. Alonso} et al., Eur. J. Appl. Math. 19, No. 5, 575--606 (2008; Zbl 1154.35428) Full Text: DOI
Aizinger, Vadym; Dawson, Clint The local discontinuous Galerkin method for three-dimensional shallow water flow. (English) Zbl 1120.76320 Comput. Methods Appl. Mech. Eng. 196, No. 4-6, 734-746 (2007). MSC: 76M10 76B15 PDFBibTeX XMLCite \textit{V. Aizinger} and \textit{C. Dawson}, Comput. Methods Appl. Mech. Eng. 196, No. 4--6, 734--746 (2007; Zbl 1120.76320) Full Text: DOI
Kubatko, Ethan J.; Westerink, Joannes J.; Dawson, Clint Hp discontinuous Galerkin methods for advection dominated problems in shallow water flow. (English) Zbl 1120.76348 Comput. Methods Appl. Mech. Eng. 196, No. 1-3, 437-451 (2006). MSC: 76M25 76B15 PDFBibTeX XMLCite \textit{E. J. Kubatko} et al., Comput. Methods Appl. Mech. Eng. 196, No. 1--3, 437--451 (2006; Zbl 1120.76348) Full Text: DOI
Dawson, Clint Analysis of discontinuous finite element methods for ground water/surface water coupling. (English) Zbl 1124.76025 SIAM J. Numer. Anal. 44, No. 4, 1375-1404 (2006). MSC: 76M10 76S05 65N30 65N15 86A05 PDFBibTeX XMLCite \textit{C. Dawson}, SIAM J. Numer. Anal. 44, No. 4, 1375--1404 (2006; Zbl 1124.76025) Full Text: DOI
Dawson, Clint; Proft, Jennifer Coupled discontinuous and continuous Galerkin finite element methods for the depth-integrated shallow water equations. (English) Zbl 1075.76570 Comput. Methods Appl. Mech. Eng. 193, No. 3-5, 289-318 (2004). MSC: 76M10 76D33 PDFBibTeX XMLCite \textit{C. Dawson} and \textit{J. Proft}, Comput. Methods Appl. Mech. Eng. 193, No. 3--5, 289--318 (2004; Zbl 1075.76570) Full Text: DOI
Dawson, Clint; Proft, Jennifer Discontinuous/continuous Galerkin methods for coupling the primitive and wave continuity equations of shallow water. (English) Zbl 1075.76569 Comput. Methods Appl. Mech. Eng. 192, No. 47-48, 5123-5145 (2003). MSC: 76M10 76B15 PDFBibTeX XMLCite \textit{C. Dawson} and \textit{J. Proft}, Comput. Methods Appl. Mech. Eng. 192, No. 47--48, 5123--5145 (2003; Zbl 1075.76569) Full Text: DOI
Dawson, Clint; Proft, Jennifer Discontinuous and coupled continuous/discontinuous Galerkin methods for the shallow water equations. (English) Zbl 1015.76046 Comput. Methods Appl. Mech. Eng. 191, No. 41-42, 4721-4746 (2002). MSC: 76M10 76B15 PDFBibTeX XMLCite \textit{C. Dawson} and \textit{J. Proft}, Comput. Methods Appl. Mech. Eng. 191, No. 41--42, 4721--4746 (2002; Zbl 1015.76046) Full Text: DOI
Dawson, Clint N.; Martínez-Canales, Mónica L. A characteristic-Galerkin approximation to a system of shallow water equations. (English) Zbl 0984.76043 Numer. Math. 86, No. 2, 239-256 (2000). MSC: 76M10 76B15 65M60 PDFBibTeX XMLCite \textit{C. N. Dawson} and \textit{M. L. Martínez-Canales}, Numer. Math. 86, No. 2, 239--256 (2000; Zbl 0984.76043) Full Text: DOI
Dawson, Clint N.; Martínez-Canales, Mónica L. Finite element approximations to the system of shallow water equations. III: On the treatment of boundary conditions. (English) Zbl 0979.35121 SIAM J. Numer. Anal. 38, No. 1, 149-159 (2000). MSC: 35Q35 76M10 65N30 65N15 35L65 PDFBibTeX XMLCite \textit{C. N. Dawson} and \textit{M. L. Martínez-Canales}, SIAM J. Numer. Anal. 38, No. 1, 149--159 (2000; Zbl 0979.35121) Full Text: DOI
Chippada, S.; Dawson, C. N.; Martínez, M. L.; Wheeler, M. F. A projection method for constructing a mass conservative velocity field. (English) Zbl 0953.76045 Comput. Methods Appl. Mech. Eng. 157, No. 1-2, 1-10 (1998). MSC: 76M10 76D33 PDFBibTeX XMLCite \textit{S. Chippada} et al., Comput. Methods Appl. Mech. Eng. 157, No. 1--2, 1--10 (1998; Zbl 0953.76045) Full Text: DOI
Chippada, S.; Dawson, C. N.; Martínez-Canales, M. L.; Wheeler, M. F. Finite element approximations to the system of shallow water equations. II: Discrete-time a priori error estimates. (English) Zbl 0958.76040 SIAM J. Numer. Anal. 36, No. 1, 226-250 (1998). Reviewer: Oleg Titow (Berlin) MSC: 76M10 76B15 65M15 PDFBibTeX XMLCite \textit{S. Chippada} et al., SIAM J. Numer. Anal. 36, No. 1, 226--250 (1998; Zbl 0958.76040) Full Text: DOI