자료유형  

 학위논문

Control Number  

0016932535

International Standard Book Number  

9798379678517

Dewey Decimal Classification Number  

300

Main Entry-Personal Name  

Yang, Jing.

Publication, Distribution, etc. (Imprint  

[S.l.] : Purdue University., 2020

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2020

Physical Description  

1 online resource(61 p.)

General Note  

Source: Dissertations Abstracts International, Volume: 84-12, Section: B.

General Note  

Advisor: Cai, Zhiqiang.

Dissertation Note  

Thesis (Ph.D.)--Purdue University, 2020.

Restrictions on Access Note  

This item must not be sold to any third party vendors.

Summary, Etc.  

요약This dissertation contains two parts: one part is about the error estimate for the finite element approximation to elliptic PDEs with discontinuous Dirichlet boundary data, the other is about the error estimate of the DG method for elliptic equations with low regularity.Elliptic problems with low regularities arise in many applications, error estimate for sufficiently smooth solutions have been thoroughly studied but few results have been obtained for elliptic problems with low regularities. Part I provides an error estimate for finite element approximation to elliptic partial differential equations (PDEs) with discontinuous Dirichlet boundary data. Solutions of problems of this type are not in H1 and, hence, the standard variational formulation is not valid. To circumvent this difficulty, an error estimate of a finite element approximation in the W1,r(Ω) (0 r 2) norm is obtained through a regularization by constructing a continuous approximation of the Dirichlet boundary data. With discontinuous boundary data, the variational form is not valid since the solution for the general elliptic equations is not in H1 . By using the W1,r (1 r 2) regularity and constructing continuous approximation to the boundary data, here we present error estimates for general elliptic equations.Part II presents a class of DG methods and proves the stability when the solution belong to H1+ε where ε 1/2 could be very small. we derive a non-standard variational formulation for advection-diffusion-reaction problems. The formulation is defined in an appropriate function space that permits discontinuity across element interfaces and does not require piece wise Hs (Ω), s ≥ 3/2, smoothness. Hence, both continuous and discontinuous (including Crouzeix-Raviart) finite element spaces may be used and are conforming with respect to this variational formulation. Then it establishes the a priori error estimates of these methods when the underlying problem is not piece wise H3/2 regular. The constant in the estimate is independent of the parameters of the underlying problem. Error analysis presented here is new. The analysis makes use of the discrete coercivity of the bilinear form, an error equation, and an efficiency bound of the continuous finite element approximation obtained in the a posteriori error estimation. Finally a new DG method is introduced i to overcome the difficulty in convergence analysis in the standard DG methods and also proves the stability.

Subject Added Entry-Topical Term  

Partial differential equations.

Subject Added Entry-Topical Term  

Error analysis.

Subject Added Entry-Topical Term  

Inequality.

Subject Added Entry-Topical Term  

Norms.

Subject Added Entry-Topical Term  

Boundary conditions.

Subject Added Entry-Topical Term  

Hilbert space.

Subject Added Entry-Topical Term  

Boundary value problems.

Subject Added Entry-Topical Term  

Mathematics.

Added Entry-Corporate Name  

Purdue University.

Host Item Entry  

Dissertations Abstracts International. 84-12B.

Host Item Entry  

Dissertation Abstract International

Electronic Location and Access  

로그인을 한후 보실 수 있는 자료입니다.

Control Number  

joongbu:643154