摘要:

We consider herein a class of problems encountered in the theory of finite plane strain of a compressible elastic body. The study is divided into two parts. In Part I, we develop several preliminary results on properties of solutions of a model boundary-value problem. We also examine briefly properties of solutions in the small (local analysis) and derive conditions on the elastic constants which guarantee the existence and uniqueness of local solutions. In Part II we consider finite element approximations of our model problem. We establish some general approximation theorems for problems of this type and, on the basis of a regularity assumption, prove some a priori error estimates.

ISSN:0163-0563    

DOI:10.1080/01630567908816003

出版商:Marcel Dekker, Inc.    

年代:1979

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630567908816004

出版商:Marcel Dekker, Inc.    

年代:1979

数据来源: Taylor

摘要:

For a two-phase Stefan problem with flux boundary conditions considered by J. R. Gannon and M. Primicerio in [l], we prove existence using Schauder's fixed point theorem. The non- linear integral operator having the fixed point property is a monotone operator in the sense of L. Collatz [2]. Therefore, we can use Schauder's theorem to construct upper and lower bounds for the free boundary. Several numerical examples demonstrate that this procedure works.

ISSN:0163-0563    

DOI:10.1080/01630567908816005

出版商:Marcel Dekker, Inc.    

年代:1979

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630567908816002

出版商:Marcel Dekker, Inc.    

年代:1979

数据来源: Taylor