Fourier stability analysis of two-dimensional finite element schemes for shallow water equations

International Journal of Computational Fluid Dynamics ◽

10.1080/10618562.2011.560572 ◽

2011 ◽

Vol 25 (2) ◽

pp. 75-94 ◽

Author(s):

Jagadeesh Anmala ◽

Rabi H. Mohtar

Keyword(s):

Finite Element ◽

Stability Analysis ◽

Shallow Water ◽

Shallow Water Equations ◽

Two Dimensional ◽

Dimensional Finite Element ◽

Finite Element Schemes

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Time-step Criteria and Fourier (von Neumann) Stability Analysis of Two-Dimensional Finite Element Schemes for Shallow Water Equations

10.13031/2013.19081 ◽

2005 ◽

Author(s):

Jagadeesh Anmala

Keyword(s):

Finite Element ◽

Stability Analysis ◽

Shallow Water Equations ◽

Two Dimensional ◽

Time Step ◽

Von Neumann ◽

Dimensional Finite Element ◽

Von Neumann Stability ◽

Von Neumann Stability Analysis ◽

Finite Element Schemes

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A NEW TWO-DIMENSIONAL FINITE ELEMENT MODEL FOR THE SHALLOW WATER EQUATIONS USING A LAGRANGIAN FRAMEWORK CONSTRUCTED ALONG FLUID PARTICLE TRAJECTORIES

International Journal for Numerical Methods in Engineering ◽

10.1002/(sici)1097-0207(19961230)39:24<4159::aid-nme52>3.0.co;2-s ◽

1996 ◽

Vol 39 (24) ◽

pp. 4159-4182 ◽

Author(s):

J. PETERA ◽

V. NASSEHI

Keyword(s):

Finite Element ◽

Finite Element Model ◽

Shallow Water ◽

Shallow Water Equations ◽

Element Model ◽

Fluid Particle ◽

Two Dimensional ◽

Particle Trajectories ◽

Lagrangian Framework ◽

Dimensional Finite Element

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Energy–enstrophy conserving compatible finite element schemes for the rotating shallow water equations with slip boundary conditions

Journal of Computational Physics ◽

10.1016/j.jcp.2018.06.071 ◽

2018 ◽

Vol 373 ◽

pp. 171-187 ◽

Author(s):

W. Bauer ◽

C.J. Cotter

Keyword(s):

Finite Element ◽

Boundary Conditions ◽

Shallow Water ◽

Shallow Water Equations ◽

Slip Boundary Conditions ◽

Slip Boundary ◽

Rotating Shallow Water ◽

Finite Element Schemes ◽

Rotating Shallow Water Equations

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Solution of the Two-Dimensional Nonlinear Shallow Water Equations Through Application of the Finite Element Flux-Corrected Transport Scheme

Computational Methods in Water Resources X - Water Science and Technology Library ◽

10.1007/978-94-010-9204-3_132 ◽

1994 ◽

pp. 1089-1096

Author(s):

Richard C. Martineau ◽

Ray A. Berry

Keyword(s):

Finite Element ◽

Shallow Water ◽

Shallow Water Equations ◽

Two Dimensional ◽

Flux Corrected Transport ◽

Nonlinear Shallow Water Equations ◽

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Testing of Finite Element Schemes for Linear Shallow Water Equations

Developments in Water Science - Computational Methods in Water Resources Vol.1 Modeling Surface and Sub-Surface Flows, Proceedings of the VII International Conference, Proceedings of the VII International Conference ◽

10.1016/s0167-5648(08)70346-0 ◽

1988 ◽

pp. 249-256 ◽

Author(s):

S.P. Kjaran ◽

S.L. Hólm ◽

S. Sigurdsson

Keyword(s):

Finite Element ◽

Shallow Water ◽

Shallow Water Equations ◽

Finite Element Schemes

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A two-dimensional finite element drying-wetting shallow water model for rivers and estuaries

Advances in Water Resources ◽

10.1016/s0309-1708(99)00031-7 ◽

2000 ◽

Vol 23 (4) ◽

pp. 359-372 ◽

Author(s):

Mourad Heniche ◽

Yves Secretan ◽

Paul Boudreau ◽

Michel Leclerc

Keyword(s):

Finite Element ◽

Shallow Water ◽

Water Model ◽

Two Dimensional ◽

Shallow Water Model ◽

Dimensional Finite Element

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Two dimensional finite element propagation and reverberation modeling in shallow water waveguides.

The Journal of the Acoustical Society of America ◽

10.1121/1.3385018 ◽

2010 ◽

Vol 127 (3) ◽

pp. 1963-1963

Author(s):

Marcia J. Isakson

Keyword(s):

Finite Element ◽

Shallow Water ◽

Two Dimensional ◽

Dimensional Finite Element

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Finite element or finite difference methods for the two-dimensional shallow water equations?

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/0045-7825(76)90068-2 ◽

1976 ◽

Vol 7 (3) ◽

pp. 351-357 ◽

Author(s):

T.J. Weare

Keyword(s):

Finite Element ◽

Finite Difference ◽

Shallow Water ◽

Shallow Water Equations ◽

Finite Difference Methods ◽

Two Dimensional ◽

Difference Methods

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Higher-order compatible finite element schemes for the nonlinear rotating shallow water equations on the sphere

Journal of Computational Physics ◽

10.1016/j.jcp.2018.08.027 ◽

2018 ◽

Vol 375 ◽

pp. 1121-1137 ◽

Author(s):

J. Shipton ◽

T.H. Gibson ◽

C.J. Cotter

Keyword(s):

Finite Element ◽

Shallow Water ◽

Shallow Water Equations ◽

Higher Order ◽

Rotating Shallow Water ◽

Finite Element Schemes ◽

Rotating Shallow Water Equations

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Bounds on Amplification Factors, Element-Node and Node-Node Equivalence for Square Finite Elements in Kinematic Shallow Water Equations

10.21203/rs.3.rs-776348/v1 ◽

2021 ◽

Author(s):

Jagadeesh Anmala ◽

Rabi H Mohtar

Keyword(s):

Finite Element ◽

Finite Elements ◽

Shallow Water ◽

Shallow Water Equations ◽

Mass Matrix ◽

Upper And Lower Bounds ◽

Nodal Solutions ◽

Lumped Mass ◽

Amplification Factors ◽

Finite Element Schemes

Abstract The upper and lower bounds of amplification factors of lumped finite element schemes are compared with nodal (integer or half-integer multiple of) eigen-value solutions of consistent finite element scheme at element and node levels of error analysis. The closeness or proximity between bounds on solutions of amplification factors and eigen-solutions reveals that the two methods, consistent and lumped finite element schemes are equivalent. The element error solutions of lumped mass matrix assumption and consistent nodal solution denotes the element-node error equivalence and the nodal solutions of all of the finite element schemes denote the node-node error equivalence for square finite elements in kinematic wave shallow water equations. The comparison plots of lumped and consistent finite element schemes are presented in this paper for illustration.

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