Page 452 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 452
MODELING, APPROXIMATION, AND ANALYSIS OF PARTIAL DIFFERENTIAL
EQUATIONS INVOLVING SINGULAR SOURCE TERMS (MS-39)
let and Neumann conditions. To ensure a meaningful formulation of such conditions, we use
the Lagrange multiplier method suitably adapted to the mixed-dimensional case. The well-
posedness of the resulting saddle-point problem is analyzed. Then, we address the numerical
approximation of the problem in the framework of the finite element method. The discretization
of the Lagrange multiplier space is the main challenge. Several options are proposed, analyzed,
and compared, with the purpose of determining a good balance between the mathematical prop-
erties of the discrete problem and flexibility of implementation of the numerical scheme. The
results are supported by evidence based on numerical experiments. The application of this
technique to microcirculation and the modeling of subsurface wells will be discussed.
450
EQUATIONS INVOLVING SINGULAR SOURCE TERMS (MS-39)
let and Neumann conditions. To ensure a meaningful formulation of such conditions, we use
the Lagrange multiplier method suitably adapted to the mixed-dimensional case. The well-
posedness of the resulting saddle-point problem is analyzed. Then, we address the numerical
approximation of the problem in the framework of the finite element method. The discretization
of the Lagrange multiplier space is the main challenge. Several options are proposed, analyzed,
and compared, with the purpose of determining a good balance between the mathematical prop-
erties of the discrete problem and flexibility of implementation of the numerical scheme. The
results are supported by evidence based on numerical experiments. The application of this
technique to microcirculation and the modeling of subsurface wells will be discussed.
450
