The Experts below are selected from a list of 219 Experts worldwide ranked by ideXlab platform
Alexis F Vasseur - One of the best experts on this subject based on the ideXlab platform.
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existence and uniqueness of strong solutions for a compressible multiphase navier stokes miscible fluid flow problem in dimension n 1
Mathematical Models and Methods in Applied Sciences, 2009Co-Authors: Craig Michoski, Alexis F VasseurAbstract:We prove the global existence and uniqueness of strong solutions for a compressible multifluid described by the barotropic Navier–Stokes equations in dim = 1. The result holds when the diffusion coefficient depends on the pressure. It relies on a global control in time of the L2 norm of the Space Derivative of the density, via a new kind of entropy.
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EXISTENCE AND UNIQUENESS OF STRONG SOLUTIONS FOR A COMPRESSIBLE MULTIPHASE NAVIER–STOKES MISCIBLE FLUID-FLOW PROBLEM IN DIMENSION n = 1
Mathematical Models and Methods in Applied Sciences, 2009Co-Authors: Craig Michoski, Alexis F VasseurAbstract:We prove the global existence and uniqueness of strong solutions for a compressible multifluid described by the barotropic Navier–Stokes equations in dim = 1. The result holds when the diffusion coefficient depends on the pressure. It relies on a global control in time of the L2 norm of the Space Derivative of the density, via a new kind of entropy.
Georgios E Zouraris - One of the best experts on this subject based on the ideXlab platform.
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An IMEX finite element method for a linearized Cahn–Hilliard–Cook equation driven by the Space Derivative of a Space–time white noise
Computational and Applied Mathematics, 2018Co-Authors: Georgios E ZourarisAbstract:We consider a model initial- and Dirichlet boundary- value problem for a linearized Cahn–Hilliard–Cook equation, in one Space dimension, forced by the Space Derivative of a Space–time white noise. First, we introduce a canvas problem, the solution to which is a regular approximation of the mild solution to the problem and depends on a finite number of random variables. Then, fully discrete approximations of the solution to the canvas problem are constructed using, for discretization in Space, a Galerkin finite element method based on $$H^2$$ H 2 piecewise polynomials, and, for time-stepping, an implicit/explicit method. Finally, we derive a strong a priori estimate of the error approximating the mild solution to the problem by the canvas problem solution, and of the numerical approximation error of the solution to the canvas problem.
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an imex finite element method for a linearized cahn hilliard cook equation driven by the Space Derivative of a Space time white noise
Computational & Applied Mathematics, 2018Co-Authors: Georgios E ZourarisAbstract:We consider a model initial- and Dirichlet boundary- value problem for a linearized Cahn–Hilliard–Cook equation, in one Space dimension, forced by the Space Derivative of a Space–time white noise. First, we introduce a canvas problem, the solution to which is a regular approximation of the mild solution to the problem and depends on a finite number of random variables. Then, fully discrete approximations of the solution to the canvas problem are constructed using, for discretization in Space, a Galerkin finite element method based on $$H^2$$ piecewise polynomials, and, for time-stepping, an implicit/explicit method. Finally, we derive a strong a priori estimate of the error approximating the mild solution to the problem by the canvas problem solution, and of the numerical approximation error of the solution to the canvas problem.
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finite element approximations for a linear cahn hilliard cook equation driven by the Space Derivative of a Space time white noise
Discrete and Continuous Dynamical Systems-series B, 2013Co-Authors: Georgios T Kossioris, Georgios E ZourarisAbstract:We consider an initial- and Dirichlet boundary- value problem for a linear Cahn-Hilliard-Cook equation, in one Space dimension, forced by the Space Derivative of a Space-time white noise. First, we propose an approximate stochastic parabolic problem discretizing the noise using linear splines. Then we construct fully-discrete approximations to the solution of the approximate problem using, for the discretization in Space, a Galerkin finite element method based on $H^2-$piecewise polynomials, and, for time-stepping, the Backward Euler method. We derive strong a priori estimates: for the error between the solution to the problem and the solution to the approximate problem, and for the numerical approximation error of the solution to the approximate problem.
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finite element approximations for a linear cahn hilliard cook equation driven by the Space Derivative of a Space time white noise
arXiv: Numerical Analysis, 2012Co-Authors: Georgios T Kossioris, Georgios E ZourarisAbstract:We consider an initial- and Dirichlet boundary- value problem for a linear Cahn-Hilliard-Cook equation, in one Space dimension, forced by the Space Derivative of a Space-time white noise. First, we propose an approximate regularized stochastic parabolic problem discretizing the noise using linear splines. Then fully-discrete approximations to the solution of the regularized problem are constructed using, for the discretization in Space, a Galerkin finite element method based on H2-piecewise polynomials, and, for time-stepping, the Backward Euler method. Finally, we derive strong a priori estimates for the modeling error and for the numerical approximation error to the solution of the regularized problem.
Craig Michoski - One of the best experts on this subject based on the ideXlab platform.
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existence and uniqueness of strong solutions for a compressible multiphase navier stokes miscible fluid flow problem in dimension n 1
Mathematical Models and Methods in Applied Sciences, 2009Co-Authors: Craig Michoski, Alexis F VasseurAbstract:We prove the global existence and uniqueness of strong solutions for a compressible multifluid described by the barotropic Navier–Stokes equations in dim = 1. The result holds when the diffusion coefficient depends on the pressure. It relies on a global control in time of the L2 norm of the Space Derivative of the density, via a new kind of entropy.
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EXISTENCE AND UNIQUENESS OF STRONG SOLUTIONS FOR A COMPRESSIBLE MULTIPHASE NAVIER–STOKES MISCIBLE FLUID-FLOW PROBLEM IN DIMENSION n = 1
Mathematical Models and Methods in Applied Sciences, 2009Co-Authors: Craig Michoski, Alexis F VasseurAbstract:We prove the global existence and uniqueness of strong solutions for a compressible multifluid described by the barotropic Navier–Stokes equations in dim = 1. The result holds when the diffusion coefficient depends on the pressure. It relies on a global control in time of the L2 norm of the Space Derivative of the density, via a new kind of entropy.
R K Mohanty - One of the best experts on this subject based on the ideXlab platform.
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high accuracy non polynomial spline in compression method for one Space dimensional quasi linear hyperbolic equations with significant first order Space Derivative term
Applied Mathematics and Computation, 2014Co-Authors: R K Mohanty, Venu GopalAbstract:Abstract In this paper, we propose a new three-level implicit nine point compact non-polynomial spline in compression finite difference method of order two in time and four in Space directions, based on non-polynomial spline approximation in x-direction and central difference approximation in t-direction for the numerical solution of one-Space dimensional second order quasi-linear hyperbolic partial differential equations with first order Space Derivative term. We describe the mathematical details of the method and also discuss how our method is able to handle wave equation in polar coordinates. The proposed method when applied to a linear hyperbolic equation is shown to be unconditionally stable. Numerical results are provided to justify the usefulness of the proposed method.
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a new high order Space Derivative discretization for 3d quasi linear hyperbolic partial differential equations
Applied Mathematics and Computation, 2014Co-Authors: R K Mohanty, Swarn SinghAbstract:Abstract In this paper, we propose a new high accuracy numerical method of O(k2 + k2h2 + h4) for the solution of three dimensional quasi-linear hyperbolic partial differential equations, where k > 0 and h > 0 are mesh sizes in time and Space directions respectively. We mainly discretize the Space Derivative terms using fourth order approximation and time Derivative term using second order approximation. We describe the derivation procedure in details and also discuss how our formulation is able to handle the wave equation in polar coordinates. The proposed method when applied to a linear hyperbolic equation is also shown to be unconditionally stable. The proposed method behaves like a fourth order method for a fixed value of ( k / h 2 ) . Some examples and their numerical results are provided to justify the usefulness of the proposed method.
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a fourth order finite difference method based on spline in tension approximation for the solution of one Space dimensional second order quasi linear hyperbolic equations
Advances in Difference Equations, 2013Co-Authors: R K Mohanty, Venu GopalAbstract:In this paper, we propose a new three-level implicit nine-point compact finite difference formulation of order two in time and four in Space directions, based on spline in tension approximation in x-direction and central finite difference approximation in t-direction for the numerical solution of one-Space dimensional second-order quasi-linear hyperbolic equations with first-order Space Derivative term. We describe the mathematical formulation procedure in detail and also discuss how our formulation is able to handle a wave equation in polar coordinates. The proposed method, when applied to a general form of the telegrapher equation, is also shown to be unconditionally stable. Numerical examples are used to illustrate the usefulness of the proposed method. MSC: 65M06; 65M12
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stability interval for explicit difference schemes for multi dimensional second order hyperbolic equations with significant first order Space Derivative terms
Applied Mathematics and Computation, 2007Co-Authors: R K MohantyAbstract:In this piece of work, we introduce a new idea and obtain stability interval for explicit difference schemes of O(k2+h2) for one, two and three Space dimensional second-order hyperbolic equations utt=a(x,t)uxx+α(x,t)ux-2η2(x,t)u,utt=a(x,y,t)uxx+b(x,y,t)uyy+α(x,y,t)ux+β(x,y,t)uy-2η2(x,y,t)u, and utt=a(x,y,z,t)uxx+b(x,y,z,t)uyy+c(x,y,z,t)uzz+α(x,y,z,t)ux+β(x,y,z,t)uy+γ(x,y,z,t)uz-2η2(x,y,z,t)u,0 0 subject to appropriate initial and Dirichlet boundary conditions, where h>0 and k>0 are grid sizes in Space and time coordinates, respectively. A new idea is also introduced to obtain explicit difference schemes of O(k2) in order to obtain numerical solution of u at first time step in a different manner.
Hans J. Haubold - One of the best experts on this subject based on the ideXlab platform.
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Computable Solutions of Fractional Reaction-Diffusion Equations Associated with Generalized Riemann-Liouville Fractional Derivatives of Fractional Orders
arXiv: Mathematical Physics, 2015Co-Authors: Ram K. Saxena, Arak M. Mathai, Hans J. HauboldAbstract:This paper is in continuation of the authors’ recently published paper (Journal of Mathematical Physics 55(2014)083519) in which computational solutions of an unified reactiondiffusion equation of distributed order associated with Caputo Derivatives as the timeDerivative and Riesz-Feller Derivative as Space Derivative is derived. In the present paper, computable solutions of distributed order fractional reaction-diffusion equations associated with generalized Riemann-Liouville Derivatives of fractional orders as the time-Derivative and Riesz-Feller fractional Derivative as the Space Derivative are investigated. The solutions of the fractional reaction-diffusion equations of fractional orders are obtained in this paper. The method followed in deriving the solutions is that of joint Laplace and Fourier transforms. The solutions obtained are in a closed and computable form in terms of the familiar generalized Mittag-Leffler functions. They provide elegant extensions of the results given in the literature.
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Further solutions of fractional reaction-diffusion equations in terms of the H-function
arXiv: Statistical Mechanics, 2011Co-Authors: Hans J. Haubold, Arak M. Mathai, Ram K. SaxenaAbstract:This paper is a continuation of our earlier paper in which we have derived the solution of an unified fractional reaction-diffusion equation associated with the Caputo Derivative as the time-Derivative and the Riesz-Feller fractional Derivative as the Space-Derivative. In this paper, we consider an unified reaction-diffusion equation with Riemann-Liouville fractional Derivative as the time-Derivative and Riesz-Feller Derivative as the Space-Derivative. The solution is derived by the application of the Laplace and Fourier transforms in a compact and closed form in terms of the H-function. The results derived are of general character and include the results investigated earlier by Kilbas et al. (2006a), Saxena et al. (2006c), and Mathai et al. (2010). The main result is given in the form of a theorem. A number of interesting special cases of the theorem are also given as corollaries.
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Further solutions of fractional reaction-diffusion equations in terms of the H-function
Journal of Computational and Applied Mathematics, 2010Co-Authors: Hans J. Haubold, Arak M. Mathai, Ram K. SaxenaAbstract:This paper is in continuation of our earlier paper in which we have derived the solution of a unified fractional reaction-diffusion equation associated with the Caputo Derivative as the time-Derivative and Riesz-Feller fractional Derivative as the Space-Derivative. In this paper, we consider a unified reaction-diffusion equation with the Riemann-Liouville fractional Derivative as the time-Derivative and Riesz-Feller Derivative as the Space-Derivative. The solution is derived by the application of the Laplace and Fourier transforms in a compact and closed form in terms of the H-function. The results derived are of general character and include the results investigated earlier in [7,8]. The main result is given in the form of a theorem. A number of interesting special cases of the theorem are also given as corollaries.
