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1

Srivastava, R. An unsteady Euler scheme for the analysis of ducted propellers. American Institute of Aeronautics and Astronautics, 1992.

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2

Powell, Kenneth G. A genuinely multi-dimensional upwind cell-vertex scheme for the Euler equations. Institute for Computational Mechanics in Propulsion, 1989.

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3

Yoon, Seokkwan. An LU-SSOR scheme for the Euler and Navier-Stokes equations. American Institute of Aeronautics and Astronautics, 1987.

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4

Sidilkover, David. A genuinely multidimensional upwind scheme and efficient multigrid solver for the compressible Euler equations. Institute for Computer Applications in Science and Engineering, 1994.

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5

Coirier, William J. An adaptively-refined, Cartesian cell-based scheme for the Euler and Navier-Stokes equations. National Aeronautics and Space Administration, 1994.

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6

Moitra, Anutosh. Application of a Runge-Kutta scheme for high-speed inviscid internal flows. ICASE, 1986.

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7

United States. National Aeronautics and Space Administration, ed. An LU-SSOR scheme for the Euler and Navier-Stokes equations. National Aeronautics and Space Administration, 1986.

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8

United States. National Aeronautics and Space Administration, ed. An LU-SSOR scheme for the Euler and Navier-Stokes equations. National Aeronautics and Space Administration, 1986.

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9

United States. National Aeronautics and Space Administration., ed. An LU-SSOR scheme for the Euler and Navier-Stokes equations. National Aeronautics and Space Administration, 1986.

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10

An LU-SSOR scheme for the Euler and Navier-Stokes equations. National Aeronautics and Space Administration, 1986.

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11

United States. National Aeronautics and Space Administration., ed. An adaptively-refined, Cartesian cell-based scheme for the Euler and Navier-Stokes equations. National Aeronautics and Space Administration, 1994.

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12

W, Swafford Timothy, Reddy T. S. R, and Lewis Research Center, eds. Euler flow predictions for an oscillating cascade using a high resolution wave-split scheme. National Aeronautics and Space Administration, Lewis Research Center, 1991.

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13

1934-, Jameson Antony, and United States. National Aeronautics and Space Administration, eds. An multigrid LU-SSOR scheme for approximate Newton iteration applied to the Euler equations. National Aeronautics and Space Administration, 1986.

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14

1934-, Jameson Antony, and United States. National Aeronautics and Space Administration, eds. An multigrid LU-SSOR scheme for approximate Newton iteration applied to the Euler equations. National Aeronautics and Space Administration, 1986.

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15

An adaptively-refined, Cartesian cell-based scheme for the Euler and Navier-Stokes equations. National Aeronautics and Space Administration, 1994.

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16

1934-, Jameson Antony, and United States. National Aeronautics and Space Administration., eds. An multigrid LU-SSOR scheme for approximate Newton iteration applied to the Euler equations. National Aeronautics and Space Administration, 1986.

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17

United States. National Aeronautics and Space Administration., ed. An adaptively-refined, Cartesian cell-based scheme for the Euler and Navier-Stokes equations. National Aeronautics and Space Administration, 1994.

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18

An multigrid LU-SSOR scheme for approximate Newton iteration applied to the Euler equations. National Aeronautics and Space Administration, 1986.

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19

Kyle, Anderson W., Roberts Thomas W, and Langley Research Center, eds. The upwind control volume scheme for unstructured triangular grids. National Aeronautics and Space Administration, Langley Research Center, 1989.

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20

Isett, Philip. Structure of the Book. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0002.

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This chapter provides an overview of the book's structure. Section 3 deals with the error terms which need to be controlled, whereas Part III explains some notation of the book and presents a basic construction of the correction. The goal is to clarify how the scheme can be used to construct Hölder continuous weak solutions—continuous in space and time—to the incompressible Euler equations that fail to conserve energy. Part IV shows how to iterate the construction of Part III to obtain continuous solutions to the Euler equations. It then discusses the concept of frequency energy levels, along
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21

Isett, Philip. Frequency and Energy Levels. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0009.

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This chapter shows how to measure the Hölder regularity of the weak solutions that are constructed when the scheme is executed more carefully. For this aspect of the convex integration scheme, a notion of frequency energy levels is introduced. This notion is meant to accurately record the bounds which apply to the (v, p, R) coming from the previous stage of the construction. The chapter presents an example of a candidate definition for frequency and energy levels. Based on this definition, the effect of one iteration of the convex integration procedure can be summarized in a single lemma, whic
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