INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 0000; 00:2–33 Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nme Coupling of polynomial approximations with application to a boundary meshless method Yendoubouam TAMPANGO 1,3 , Michel POTIER-FERRY 1,2* , Yao KOUTSAWA 3 and Sonnou TIEM 4 1 LEM3, Laboratoire d’ Etude des Microstructures et de Mécanique des Matériaux, UMR CNRS 7239, Université de Lorraine, Ile du Saulcy, 57045 Metz Cedex 01, France 2 Laboratory of Excellence on Design of Alloy Metals for low-mAss Structures (DAMAS), Université de Lorraine, France 3 CRP Henri Tudor, 66, rue de Luxembourg, L-4221 Esch-sur-Alzette, Luxembourg 4 Ecole Nationale Supérieure d’Ingénieurs de Lomé, Université de Lomé, BP 1515 Lomé Togo SUMMARY New bridging techniques are introduced to match high degree polynomials. This permits piecewise resolutions of elliptic Partial Differential Equations in the framework of a boundary meshless method introduced recently. This new meshless method relies on the computation of Taylor series approximations deduced from the PDE, the shape functions being high degree polynomials. In this way, the PDE is solved quasi-exactly inside the subdomains so that only discretisation of the boundary and the interfaces are needed, which leads to small size matricial problems. The bridging techniques are based on the introduction of Lagrange multipliers and a set of collocation points on the boundary and the interfaces. Several numerical applications establish that the method is robust and permits an exponential convergence with the degree. Copyright c  0000 John Wiley & Sons, Ltd. Received . . . KEY WORDS: Taylor series; Meshless; domain decomposition; Arlequin; Bridging Copyright c  0000 John Wiley & Sons, Ltd. Prepared using nmeauth.cls [Version: 2010/05/13 v3.00]