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In this paper, we propose a new stabilized linear finite element method for solving reaction–convection–diffusion equations with arbitrary magnitudes of reaction and diffusion. The key feature of the new method is that the test function in the stabilization term is taken in the adjoint-operator-like form −εΔv−(a⋅∇v)/γ+σv, where the parameter γ is appropriately designed to adjust the convection strength...
In this paper, we propose and analyze a new stabilized finite element method using continuous piecewise linear (or bilinear) elements for solving 2D reaction–convection–diffusion equations. The equation under consideration involves a small diffusivity ε and a large reaction coefficient σ, leading to high Péclet number and high Damköhler number. In addition to giving error estimates of the approximations...
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