UPWIND FINITE ELEMENT METHODS FOR H(grad), H(curl) AND H(div) CONVECTION-DIFFUSION PROBLEMS

Duration: 50 mins 9 secs

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Description:	Xu, J Tuesday 22nd October 2019 - 13:55 to 14:40


Created:	2019-10-22 14:56
Collection:	Geometry, compatibility and structure preservation in computational differential equations
Publisher:	Isaac Newton Institute
Copyright:	Xu, J
Language:	eng (English)


Abstract:	This talk is devoted to the construction and analysis of the finite element approximations for the H(grad), H(curl) and H(div) convection-diffusion problems. An essential feature of these constructions is to properly average the PDE coefficients on sub-simplexes from the underlying simplicial finite element meshes. The schemes are of the class of exponential fitting methods that result in special upwind schemes when the diffusion coefficient approaches to zero. Their well-posedness are established for sufficiently small mesh size assuming that the convection-diffusion problems are uniquely solvable. Convergence of first order is derived under minimal smoothness of the solution. Some numerical examples are given to demonstrate the robustness and effectiveness for general convection-diffusion problems. This is a joint work with Shounan Wu.

Abstract:

This talk is devoted to the construction and analysis of the finite element approximations for the H(grad), H(curl) and H(div) convection-diffusion problems. An essential feature of these constructions is to properly average the PDE coefficients on sub-simplexes from the underlying simplicial finite element meshes. The schemes are of the class of exponential fitting methods that result in special upwind schemes when the diffusion coefficient approaches to zero. Their well-posedness are established for sufficiently small mesh size assuming that the convection-diffusion problems are uniquely solvable. Convergence of first order is derived under minimal smoothness of the solution. Some numerical examples are given to demonstrate the robustness and effectiveness for general convection-diffusion problems. This is a joint work with Shounan Wu.

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