The Singular Complement Method

The philosophy of the SCM is different, although the tools are similar: the idea is still to split the space , but with respect to regularity. Indeed, elements of belong to the scale of Sobolev spaces 576 98 , or 5:6 ;8 =< , where 8?>A@ < is the computational domain, and BC @ED . Interestingly, for a given space , the supremum B FEG H of all possible values of the exponent B , depends on the convexity of the domain and on the smoothness of its boundary. Let BEI be the supremum when the domain is convex, or smooth. When the domain is non-convex and non-smooth, B FEG HKJLBMI usually holds. Then, let )N7 O P15Q6SR 98 (or )NT P15Q6SR ;8 =< for vector fields) be the space of regular elements. Assume that UN is closed in , and let O N V UW (4)

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