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M2AN_2007__41_1_55_0.pdf
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👤 Author: EDPSciences
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Summary

A continuous finite element method with face penalty is proposed to approximate Friedrichs' systems, which are systems of first-order PDEs with symmetry and positivity properties. The method stabilizes the continuous finite element approximation by penalizing the jumps of the normal derivative of some components of the discrete solution across mesh interfaces. The convergence analysis leads to optimal convergence rates in the graph norm and suboptimal convergence rates in the L2-norm. A variant of the method is also proposed for Friedrichs' systems associated with elliptic PDEs in mixed form, which reduces the number of nonzero entries in the stiffness matrix. Numerical results illustrate the theoretical analysis and show that the face penalty technique can effectively control oscillations produced by the continuous finite element method without stabilization.

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A continuous finite element method with face penalty is proposed to approximate Friedrichs' systems, which are systems of first-order PDEs with symmetry and...

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  • File Format: PDF
  • File Size: 488 KB
  • Pages: 22
  • Language: EN
  • Author: EDPSciences
  • Total Downloads: 116
  • Last Updated: 3 weeks ago

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