Blending low-order stabilised finite element methods: a positivity-preserving local projection method for the convection-diffusion equation
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In this work we propose a nonlinear blending of two low-order stabilisation mechanisms for the convection-diffusion equation. The motivation for this approach is to preserve monotonicity without sacrificing accuracy for smooth solutions. The approach is to blend a first-order artificial diffusion method, which will be active only in the vicinity of layers and extrema, with an optimal order local projection stabilisation method that will be active on the smooth regions of the solution. We prove existence of discrete solutions, as well as convergence, under appropriate assumptions on the nonlinear terms, and on the exact solution. Numerical examples show that the discrete solution produced by this method remains within the bounds given by the continuous maximum principle, while the layers are not smeared significantly.
|Number of pages||25|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|Early online date||20 Jan 2017|
|State||E-pub ahead of print - 20 Jan 2017|
- discrete maximum principle, convection-diffusion equation, nonlinear scheme, local projection stabilisation