The p-Version of the Finite Element Method for Parabolic Equations. Part 1

Abstract : The finite element method has become the main tool in computational mechanics. The MAKABASE contains about 20,000 references on finite element and 2000 boundary element technology. Recently the new direction in the finite element theory and practice appeared, the p and h-p versions, which utilize high degree of elements. About 3 - 4 dozen references about p and h-p versions are available, all of them related to the elliptic problems. For the survey of today's state of the art, we refer to e.g. This paper addresses the basic problems of the p-version for the parabolic equation with both variables, x and t discreted via p-version. It concentrates on the case when in the time variables only one interval is used. The paper gives the error estimates and presents some numerical aspects. The authors restrict themselves to the basic features of the method. Various generalizations will be presented in forthcoming papers.