
Finite element method with the total stress variable for Biot's consolidation model
In this work, semidiscrete and fullydiscrete error estimates are deriv...
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Decoupling schemes for predicting compressible fluid flows
Numerical simulation of compressible fluid flows is performed using the ...
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Analysis of a fully discrete approximation for the classical Keller–Segel model: lower and a priori bounds
This paper is devoted to constructing approximate solutions for the clas...
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Highorder spacetime finite element methods for the PoissonNernstPlanck equations: Positivity and unconditional energy stability
We present a novel class of highorder spacetime finite element schemes...
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Assessment of a nonconservative fourequation multiphase system with phase transition
This work focuses on the formulation of a fourequation model for simula...
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Staggered Residual Distribution scheme for compressible flow
This paper is focused on the approximation of the Euler equation of comp...
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A macroelement stabilization for multiphase poromechanics
Strong coupling between geomechanical deformation and multiphase fluid f...
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A Conservative Finite Element Method for the Incompressible Euler Equations with Variable Density
We construct a finite element discretization and timestepping scheme for the incompressible Euler equations with variable density that exactly preserves total mass, total squared density, total energy, and pointwise incompressibility. The method uses RaviartThomas or BrezziDouglasMarini finite elements to approximate the velocity and discontinuous polynomials to approximate the density and pressure. To achieve exact preservation of the aforementioned conserved quantities, we exploit a seldomused weak formulation of the momentum equation and a secondorder timestepping scheme that is similar, but not identical, to the midpoint rule. We also describe and prove stability of an upwinded version of the method. We present numerical examples that demonstrate the order of convergence of the method.
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