The Experts below are selected from a list of 327 Experts worldwide ranked by ideXlab platform
Kazunori Matsui - One of the best experts on this subject based on the ideXlab platform.
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Analysis of a projection method for the Stokes Problem using an $$\varepsilon $$ ε -Stokes approach
Japan Journal of Industrial and Applied Mathematics, 2019Co-Authors: Masato Kimura, Kazunori Matsui, Adrian Muntean, Hirofumi NotsuAbstract:We generalize pressure boundary conditions of an $$\varepsilon $$ -Stokes Problem. Our $$\varepsilon $$ -Stokes Problem connects the classical Stokes Problem and the corresponding pressure-Poisson equation using one parameter $$\varepsilon >0$$ . For the Dirichlet boundary condition, it is proven in Matsui and Muntean (Adv Math Sci Appl, 27:181–191, 2018) that the solution for the $$\varepsilon $$ -Stokes Problem converges to the one for the Stokes Problem as $$\varepsilon $$ tends to 0, and to the one for the pressure-Poisson Problem as $$\varepsilon $$ tends to $$\infty $$ . Here, we extend these results to the Neumann and mixed boundary conditions. We also establish error estimates in suitable norms between the solutions to the $$\varepsilon $$ -Stokes Problem, the pressure-Poisson Problem and the Stokes Problem, respectively. Several numerical examples are provided to show that several such error estimates are optimal in $$\varepsilon $$ . Our error estimates are improved if one uses the Neumann boundary conditions. In addition, we show that the solution to the $$\varepsilon $$ -Stokes Problem has a nice asymptotic structure.
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Asymptotic analysis of an ε-Stokes Problem with Dirichlet boundary conditions
2019Co-Authors: Kazunori MatsuiAbstract:In this thesis, we propose an e-Stokes Problem connecting the Stokes Problem and the corresponding pressure-Poisson equation using one pa- rameter e > 0. We prove that the solution to the e-Stok ...
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Analysis of a projection method for the Stokes Problem using an $\varepsilon$-Stokes approach
arXiv: Analysis of PDEs, 2018Co-Authors: Masato Kimura, Kazunori Matsui, Adrian Muntean, Hirofumi NotsuAbstract:We generalize pressure boundary conditions of an $\varepsilon$-Stokes Problem. Our $\varepsilon$-Stokes Problem connects the classical Stokes Problem and the corresponding pressure-Poisson equation using one parameter $\varepsilon>0$. For the Dirichlet boundary condition, it is proven in K. Matsui and A. Muntean (2018) that the solution for the $\varepsilon$-Stokes Problem converges to the one for the Stokes Problem as $\varepsilon$ tends to 0, and to the one for the pressure-Poisson Problem as $\varepsilon$ tends to $\infty$. Here, we extend these results to the Neumann and mixed boundary conditions. We also establish error estimates in suitable norms between the solutions to the $\varepsilon$-Stokes Problem, the pressure-Poisson Problem and the Stokes Problem, respectively. Several numerical examples are provided to show that several such error estimates are optimal in $\varepsilon$. Our error estimates are improved if one uses the Neumann boundary conditions. In addition, we show that the solution to the $\varepsilon$-Stokes Problem has a nice asymptotic structure.
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Boundary conditions for the Stokes Problem and a pressure-Poisson Problem
arXiv: Analysis of PDEs, 2018Co-Authors: Kazunori MatsuiAbstract:We consider a boundary value Problem for the stationary Stokes Problem and the corresponding pressure-Poisson equation. We propose a new formulation for the pressure-Poisson Problem with an appropriate additional boundary condition. We establish error estimates between solutions to the Stokes Problem and the pressure-Poisson Problem in terms of the additional boundary condition. As boundary conditions for the Stokes Problem, we use a traction boundary condition and a pressure boundary condition introduced in C. Conca et al (1994).
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Asymptotic analysis of an $\varepsilon$-Stokes Problem connecting Stokes and pressure-Poisson Problems
arXiv: Analysis of PDEs, 2017Co-Authors: Kazunori Matsui, Adrian MunteanAbstract:In this Note, we prepare an $\varepsilon$-Stokes Problem connecting the Stokes Problem and the corresponding pressure-Poisson equation using one parameter $\varepsilon>0$. We prove that the solution to the $\varepsilon$-Stokes Problem, convergences as $\varepsilon$ tends to 0 or $\infty$ to the Stokes and pressure-Poisson Problem, respectively.
François Dubois - One of the best experts on this subject based on the ideXlab platform.
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vorticity velocity pressure and stream function vorticity formulations for the Stokes Problem
Journal de Mathématiques Pures et Appliquées, 2003Co-Authors: François Dubois, Michel Salaun, Stephanie SalmonAbstract:Abstract We study the Stokes Problem of incompressible fluid dynamics in two and three-dimension spaces, for general bounded domains with smooth boundary. We use the vorticity–velocity-pressure formulation and introduce a new Hilbert space for the vorticity. We develop an abstract mixed formulation that gives a precise variational frame and conducts to a well-posed Stokes Problem involving a new velocity–vorticity boundary condition. In the particular case of simply connected bidimensional domains with homogeneous boundary conditions, the link with the classical stream function-vorticity formulation is completely described, and we show that the vorticity–velocity-pressure formulation is a natural mathematical extension of the previous one.
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Discrete harmonics for stream function-vorticity Stokes Problem
Numerische Mathematik, 2002Co-Authors: Stephanie Salmon, François Dubois, Michel SalaunAbstract:We consider the bidimensional Stokes Problem for incompressible fluids in stream function-vorticity. For this Problem, the classical finite element method of degree one converges only in O(Öh) for the L2-norm of the vorticity. We propose to use harmonic functions to approach the vorticity along the boundary. Discrete harmonics are functions that are used in practice to derive a new numerical method. We prove that we obtain with this numerical scheme an error of order O(h) for the L2-norm of the vorticity.
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Vorticity-velocity-pressure formulation for the Stokes Problem
Mathematical Methods in the Applied Sciences, 2002Co-Authors: François DuboisAbstract:We present a new variational formulation of Stokes Problem of fluid mechanics that allows to take into account very general boundary conditions for velocity, tangential vorticity or pressure. This formulation conducts a well posed mathematical Problem in a family of particular cases.
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Discrete harmonics for the Stokes Problem
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2000Co-Authors: François Dubois, Michel Salaun, Stephanie SalmonAbstract:Abstract We consider the bidimensional Stokes Problem for incompressible fluids in stream function-vorticity. For this Problem, the classical finite elements method of degree one converges as O ( h T ) in the L 2 -norm of the vorticity. We propose to use harmonic functions to approach the vorticity along the boundary. Discrete harmonics are functions that are used in practice to derive a new numerical method. We obtain with this numerical scheme an error of order O (h 1−e T ) , e >0, for the L 2 -norm of the vorticity and present a first numerical test.
Stephanie Salmon - One of the best experts on this subject based on the ideXlab platform.
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vorticity velocity pressure and stream function vorticity formulations for the Stokes Problem
Journal de Mathématiques Pures et Appliquées, 2003Co-Authors: François Dubois, Michel Salaun, Stephanie SalmonAbstract:Abstract We study the Stokes Problem of incompressible fluid dynamics in two and three-dimension spaces, for general bounded domains with smooth boundary. We use the vorticity–velocity-pressure formulation and introduce a new Hilbert space for the vorticity. We develop an abstract mixed formulation that gives a precise variational frame and conducts to a well-posed Stokes Problem involving a new velocity–vorticity boundary condition. In the particular case of simply connected bidimensional domains with homogeneous boundary conditions, the link with the classical stream function-vorticity formulation is completely described, and we show that the vorticity–velocity-pressure formulation is a natural mathematical extension of the previous one.
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Discrete harmonics for stream function-vorticity Stokes Problem
Numerische Mathematik, 2002Co-Authors: Stephanie Salmon, François Dubois, Michel SalaunAbstract:We consider the bidimensional Stokes Problem for incompressible fluids in stream function-vorticity. For this Problem, the classical finite element method of degree one converges only in O(Öh) for the L2-norm of the vorticity. We propose to use harmonic functions to approach the vorticity along the boundary. Discrete harmonics are functions that are used in practice to derive a new numerical method. We prove that we obtain with this numerical scheme an error of order O(h) for the L2-norm of the vorticity.
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Discrete harmonics for the Stokes Problem
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2000Co-Authors: François Dubois, Michel Salaun, Stephanie SalmonAbstract:Abstract We consider the bidimensional Stokes Problem for incompressible fluids in stream function-vorticity. For this Problem, the classical finite elements method of degree one converges as O ( h T ) in the L 2 -norm of the vorticity. We propose to use harmonic functions to approach the vorticity along the boundary. Discrete harmonics are functions that are used in practice to derive a new numerical method. We obtain with this numerical scheme an error of order O (h 1−e T ) , e >0, for the L 2 -norm of the vorticity and present a first numerical test.
Adrian Muntean - One of the best experts on this subject based on the ideXlab platform.
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Analysis of a projection method for the Stokes Problem using an $$\varepsilon $$ ε -Stokes approach
Japan Journal of Industrial and Applied Mathematics, 2019Co-Authors: Masato Kimura, Kazunori Matsui, Adrian Muntean, Hirofumi NotsuAbstract:We generalize pressure boundary conditions of an $$\varepsilon $$ -Stokes Problem. Our $$\varepsilon $$ -Stokes Problem connects the classical Stokes Problem and the corresponding pressure-Poisson equation using one parameter $$\varepsilon >0$$ . For the Dirichlet boundary condition, it is proven in Matsui and Muntean (Adv Math Sci Appl, 27:181–191, 2018) that the solution for the $$\varepsilon $$ -Stokes Problem converges to the one for the Stokes Problem as $$\varepsilon $$ tends to 0, and to the one for the pressure-Poisson Problem as $$\varepsilon $$ tends to $$\infty $$ . Here, we extend these results to the Neumann and mixed boundary conditions. We also establish error estimates in suitable norms between the solutions to the $$\varepsilon $$ -Stokes Problem, the pressure-Poisson Problem and the Stokes Problem, respectively. Several numerical examples are provided to show that several such error estimates are optimal in $$\varepsilon $$ . Our error estimates are improved if one uses the Neumann boundary conditions. In addition, we show that the solution to the $$\varepsilon $$ -Stokes Problem has a nice asymptotic structure.
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Analysis of a projection method for the Stokes Problem using an $\varepsilon$-Stokes approach
arXiv: Analysis of PDEs, 2018Co-Authors: Masato Kimura, Kazunori Matsui, Adrian Muntean, Hirofumi NotsuAbstract:We generalize pressure boundary conditions of an $\varepsilon$-Stokes Problem. Our $\varepsilon$-Stokes Problem connects the classical Stokes Problem and the corresponding pressure-Poisson equation using one parameter $\varepsilon>0$. For the Dirichlet boundary condition, it is proven in K. Matsui and A. Muntean (2018) that the solution for the $\varepsilon$-Stokes Problem converges to the one for the Stokes Problem as $\varepsilon$ tends to 0, and to the one for the pressure-Poisson Problem as $\varepsilon$ tends to $\infty$. Here, we extend these results to the Neumann and mixed boundary conditions. We also establish error estimates in suitable norms between the solutions to the $\varepsilon$-Stokes Problem, the pressure-Poisson Problem and the Stokes Problem, respectively. Several numerical examples are provided to show that several such error estimates are optimal in $\varepsilon$. Our error estimates are improved if one uses the Neumann boundary conditions. In addition, we show that the solution to the $\varepsilon$-Stokes Problem has a nice asymptotic structure.
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Asymptotic analysis of an $\varepsilon$-Stokes Problem connecting Stokes and pressure-Poisson Problems
arXiv: Analysis of PDEs, 2017Co-Authors: Kazunori Matsui, Adrian MunteanAbstract:In this Note, we prepare an $\varepsilon$-Stokes Problem connecting the Stokes Problem and the corresponding pressure-Poisson equation using one parameter $\varepsilon>0$. We prove that the solution to the $\varepsilon$-Stokes Problem, convergences as $\varepsilon$ tends to 0 or $\infty$ to the Stokes and pressure-Poisson Problem, respectively.
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Asymptotic analysis of an $\varepsilon$-Stokes Problem connecting Stokes and pressure-Poisson Problems
2017Co-Authors: Kazunori Matsui, Adrian MunteanAbstract:In this Note, we prepare an e-Stokes Problem connecting the Stokes Problem and the corresponding pressure-Poisson equation using one parameter e > 0. We prove that the solution to the e-Stokes p ...
Michel Salaun - One of the best experts on this subject based on the ideXlab platform.
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vorticity velocity pressure and stream function vorticity formulations for the Stokes Problem
Journal de Mathématiques Pures et Appliquées, 2003Co-Authors: François Dubois, Michel Salaun, Stephanie SalmonAbstract:Abstract We study the Stokes Problem of incompressible fluid dynamics in two and three-dimension spaces, for general bounded domains with smooth boundary. We use the vorticity–velocity-pressure formulation and introduce a new Hilbert space for the vorticity. We develop an abstract mixed formulation that gives a precise variational frame and conducts to a well-posed Stokes Problem involving a new velocity–vorticity boundary condition. In the particular case of simply connected bidimensional domains with homogeneous boundary conditions, the link with the classical stream function-vorticity formulation is completely described, and we show that the vorticity–velocity-pressure formulation is a natural mathematical extension of the previous one.
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Discrete harmonics for stream function-vorticity Stokes Problem
Numerische Mathematik, 2002Co-Authors: Stephanie Salmon, François Dubois, Michel SalaunAbstract:We consider the bidimensional Stokes Problem for incompressible fluids in stream function-vorticity. For this Problem, the classical finite element method of degree one converges only in O(Öh) for the L2-norm of the vorticity. We propose to use harmonic functions to approach the vorticity along the boundary. Discrete harmonics are functions that are used in practice to derive a new numerical method. We prove that we obtain with this numerical scheme an error of order O(h) for the L2-norm of the vorticity.
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Discrete harmonics for the Stokes Problem
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2000Co-Authors: François Dubois, Michel Salaun, Stephanie SalmonAbstract:Abstract We consider the bidimensional Stokes Problem for incompressible fluids in stream function-vorticity. For this Problem, the classical finite elements method of degree one converges as O ( h T ) in the L 2 -norm of the vorticity. We propose to use harmonic functions to approach the vorticity along the boundary. Discrete harmonics are functions that are used in practice to derive a new numerical method. We obtain with this numerical scheme an error of order O (h 1−e T ) , e >0, for the L 2 -norm of the vorticity and present a first numerical test.