Variational formulation of linear problems with nonhomogeneous boundary conditions and internal discontinuities

• Published in: Computer methods in applied mechanics and engineering Vol. 7; no. 1; pp. 75 - 91
• Main Authors: Sandhu, Ranbir S., Salaam, U.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 1976
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/0045-7825(76)90006-2

A variational formulation applicable to linear operators with nonhomogeneous boundary conditions and jump discontinuities is presented. For the formulation to be applicable, the boundary condition and discontinuities have to be consistent with the operator governing the field problem. The problem is set up in a space of suitable continuous bilinear mapping. Thus, operators on inner product spaces, convolution spaces and energy spaces are included as specializations. The basic construction can be used to generate dual-complementary variational principles. Implementation is illustrated by examples. The role of boundary terms in finite element discretizations based on interpolants of limited smoothness is discussed.