Introduction.- Motivation and Background.- Overview of
Existing Methods.- One-Dimensional Problems.- Interpolation in
One Dimension.- Numerical Integration in One
Dimension.- 1D Continuous Galerkin Method for Hyperbolic
Equations.- 1D Discontinuous Galerkin Methods for Hyperbolic
Equations.- 1D Unified Continuous and Discontinuous Galerkin
Methods for
Systems of Hyperbolic Equations.- 1D Continuous Galerkin Methods
for Elliptic Equations.- 1D Discontinuous Galerkin Methods for
Elliptic Equations.- Two-Dimensional Problems.- Interpolation
in Multiple Dimensions.- Numerical Integration in Multiple
Dimensions.- 2D Continuous Galerkin Methods for Elliptic
Equations.- 2D Discontinuous Galerkin Methods for Elliptic
Equations.- 2D Unified Continuous and Discontinuous Galerkin
Methods for Elliptic Equations.- 2D Continuous Galerkin Methods for
Hyperbolic Equations.- 2D Discontinuous Galerkin Methods for
Hyperbolic Equations.- 2D Continuous/Discontinuous Galerkin
Methods for Hyperbolic Equations.- Advanced
Topics.- Stabilization of High-Order Methods.- Adaptive
Mesh Refinement.- Time Integration.- 1D Hybridizable
Discontinuous Galerkin Method.- Classification of Partial
Differential Equations and Vector Notation.- Jacobi
Polynomials.- Data Structures.
Francis (Frank) Giraldo is a Distinguished Professor of Applied Mathematics at the Naval Postgraduate School and a founding member of the Scientific Computing group. He and his team built the NUMA model using the element-based Galerkin (EBG) methods described in this text; NUMA is a Navier-Stokes solver used for atmospheric, ocean, and fluid dynamics simulations. Frank Giraldo (and colleagues) hosted the 2012 Gene Golub SIAM Summer School on Simulation and Supercomputing in the Geosciences where EBG methods was one of the topics of the summer course. In addition, Frank has served on the National Earth Systems Prediction Capability working groups for over 10 years, and has served on the Department of Energy’s INCITE panels for over 5 years (including chairing the committee a number of times).
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