ABSTRACT
P. BURDA Dept . of Math. , Fac. Mech. Eng . , Czech Tech. Univ. , Karlovo namesti 13 , CZ-12135 Prague 2, Czech Republic
Abstract . The problem of interfaces and singularities is presented on the model elliptic equation on the square n c E2 cut into four subsquares . The prob lem of interfaces is studied first . We consider that there is no singularity in n. On triangles we use cubic Hermitean polynomials . On the interfaces we suggest the technique of coupling of parameters corresponding to derivatives which have to satisfy the interface condition. We show the convergence of the method of coupling of interface parameters and give some numerical results , to show the advantages of our technique over the standard method of free parameters . The prob lem of internal s ingularities is studied in the second part of the paper. Now we consider that there is a singularity at the central point of the domain n. Again cubic Hermitean elements are suggested, with one exception: on the triangle whose vertex coincides with the singular point (where the derivatives of solution are infinite) we propose new type of element , in fact a hybrid of Lagrangean and Hermitean element , denoted by H2L1 . Numerical experiments show that , if the singularity is not too strong then H2Ll elements give sufficiently precise results . The influence of the strength of the singularity on the error is shown.
