A POSTERIORI ERROR ESTIMATION OF hpk FE SOLUTIONS OF LINEAR BOUNDARY VALUE PROBLEMS IN TERMS OF QUANTITIES OF INTEREST
The k-Version of the finite element (FE) method was first introduced by Surana et al. and is a method of approximation of partial differential equations (PDEs) that adheres to strictly using well-posed.i.e. variationally consistent,integral formulations. In addition.it constructs the FE approximations by introducing a new parameter k in addition to the conventionally used parameters h and p. The new parameter k defines a global differentiability of the approximation functions of order (k-1). Hence, the fe-Version FE method can provide FE approximations which have a global order of differentiability as desired by the PDEs or the physical phenomena described by the PDEs. The resulting,so-called hpk FE processes are robust and show remarkable accuracy (versus computational cost) regardless whether the differential operators appearing in the PDEs are selfadjoint, non-selfadjoint, or non-linear. The robustness, which is established by using strictly variationally consistent integral formulations,also leads to an accurate and reliable framework for the a posteriori estimation of numerical approximation errors incurred by the hpk FE analyses. We present a posteriori error estimates for the numerical analysis of linear boundary value problems of second order PDEs. Estimates in terms of quantities of interest are introduced for the case in which the PDEs involve selfadjoint or non-selfadjoint operators. Two-dimensional numerical verifications are presented for a set of two model problems consisting of a diffusion as well as a convection-diffusion equation with dominant convective terms.
finite element methods higher order global differentiability approximations error estimation
Romkes A Bryant C M Surana K S
Department of Mechanical Engineering, University of Kansas, Lawrence, Kansas, USA Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Tex
国际会议
广州
英文
122-127
2010-12-17（万方平台首次上网日期，不代表论文的发表时间）