Well-Posedness and Finite Element Approximation for the Convection Model in Superposed Fluid and Porous Layers

2020 ◽  
Vol 58 (1) ◽  
pp. 541-564 ◽  
Author(s):  
Yuhong Zhang ◽  
Li Shan ◽  
Yanren Hou
Keyword(s):  
Finite Element ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Well Posedness ◽  
Porous Layers ◽  
Convection Model

scholarly journals Well-posedness and H(div)-conforming finite element approximation of a linearised model for inviscid incompressible flow

2020 ◽  
Vol 30 (05) ◽  
pp. 847-865
Author(s):  
Gabriel Barrenechea ◽  
Erik Burman ◽  
Johnny Guzmán
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
Model Problem ◽  
Finite Element Approximation ◽  
Inviscid Flow ◽  
Element Approximation ◽  
Well Posedness ◽  
Hodge Laplacian ◽  
Conforming Finite Element ◽  
Velocity Approximation

We consider a linearised model of incompressible inviscid flow. Using a regularisation based on the Hodge Laplacian we prove existence and uniqueness of weak solutions for smooth domains. The model problem is then discretised using [Formula: see text](div)-conforming finite element methods, for which we prove error estimates for the velocity approximation in the [Formula: see text]-norm of order [Formula: see text]. We also prove error estimates for the pressure error in the [Formula: see text]-norm.

scholarly journals Well Posedness and Finite Element Approximability of Three-Dimensional Time-Harmonic Electromagnetic Problems Involving Rotating Axisymmetric Objects

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 218 ◽  
Author(s):  
Praveen Kalarickel Ramakrishnan ◽  
Mirco Raffetto
Keyword(s):  
Finite Element ◽  
Boundary Value Problems ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Well Posedness ◽  
Electromagnetic Problems ◽  
Time Harmonic ◽  
First Time

A set of sufficient conditions for the well posedness and the convergence of the finite element approximation of three-dimensional time-harmonic electromagnetic boundary value problems involving non-conducting rotating objects with stationary boundaries or bianisotropic media is provided for the first time to the best of authors’ knowledge. It is shown that it is not difficult to check the validity of these conditions and that they hold true for broad classes of practically important problems which involve rotating or bianisotropic materials. All details of the applications of the theory are provided for electromagnetic problems involving rotating axisymmetric objects.

Well-posedness of an electric interface model and its finite element approximation

2016 ◽  
Vol 26 (03) ◽  
pp. 601-625 ◽  
Author(s):  
Habib Ammari ◽  
Dehan Chen ◽  
Jun Zou
Keyword(s):  
Finite Element ◽  
Electric Fields ◽  
Finite Element Approximation ◽  
Interface Problem ◽  
Element Approximation ◽  
Well Posedness ◽  
Fully Discrete ◽  
Potential Applications ◽  
Shaped Pulse ◽  
Discrete Finite Element

This work aims at providing a mathematical and numerical framework for the analysis on the effects of pulsed electric fields on the physical media that have a heterogeneous permittivity and a heterogeneous conductivity. Well-posedness of the model interface problem and the regularity of its solutions are established. A fully discrete finite element scheme is proposed for the numerical approximation of the potential distribution as a function of time and space simultaneously for an arbitrary-shaped pulse, and it is demonstrated to enjoy the optimal convergence order in both space and time. The new results and numerical scheme have potential applications in the fields of electromagnetism, medicine, food sciences, and biotechnology.

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