We investigate moduli of planar circular quadrilaterals symmetric with respect to both the coordinate axes. First , making use the Schwarz ODE, we develop an analytic method to determine a conformal mapping the unit disk onto a given circular quadrilateral. We devise a numerical method to find  the accessory parameters , solve the equation and to compute the modulus of the quadrilateral. We also give an example of a circular quadrilateral for which the value of the conformal modulus can be found in the analytic form; this example is used to validate the numeric calculations. We also use another method, so called hp-FEM , for the numeric calculation of the moduli. These two different approaches provide results agreeing with high accuracy . An example of a quadrilateral, connected with a circular hexagon, with known modulus is considered as well .
We investigate moduli of planar circular quadrilaterals symmetric with respect to both the coordinate axes. First we develop an analytic approach which reduces this problem to ODEs and devise a numeric method to find out the accessory parameters . This method uses the Schwarz equation to determine conformal mapping of the unit disk onto a given circular quadrilateral. We also give an example of a circular quadrilateral for which the value of the conformal modulus can be found in the analytic form; this example is used to validate the numeric calculations. We also use another method, so called hpFEM , for the numeric calculation of the moduli. These two different approaches provide results agreeing with high accuracy .
D
, making use the Schwarz ODE,
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method to determine a conformal mapping the unit disk onto a given circular quadrilateral. We devise a numerical
approach which reduces this problem to ODEs and devise a numeric
A
out
R
, solve the equation and to compute the modulus of the
. This method uses the Schwarz equation to determine conformal mapping of the unit disk onto a given circular
R
hp-FEM
hpFEM
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. An example of a quadrilateral, connected with a circular hexagon, with known modulus is considered as well