TY - JOUR

T1 - Analysis of finite element approximation of evolution problems in mixed form

AU - Boffi, Daniele

AU - Gastaldi, Lucia

N1 - Generated from Scopus record by KAUST IRTS on 2020-05-05

PY - 2004/12/1

Y1 - 2004/12/1

N2 - This paper deals with the finite element approximation of evolution problems in mixed form. Following [D. Boffi, F. Brezzi, and L. Gastaldi, Math. Comp., 69 (2000), pp. 121-140], we handle separately two types of problems. A model for the first case is the heat equation in mixed form, while the time dependent Stokes problem fits within the second one. For either case, we give sufficient conditions for a good approximation in the natural functional spaces. The results are not obvious in the first situation. In this case, the well-known conditions for the well posedness and convergence of the corresponding steady problem are not sufficient for the good approximation of the time dependent problem. This issue is demonstrated with a numerical (counter-) example and justified analytically. © 2004 Society for Industrial and Applied Mathematics.

AB - This paper deals with the finite element approximation of evolution problems in mixed form. Following [D. Boffi, F. Brezzi, and L. Gastaldi, Math. Comp., 69 (2000), pp. 121-140], we handle separately two types of problems. A model for the first case is the heat equation in mixed form, while the time dependent Stokes problem fits within the second one. For either case, we give sufficient conditions for a good approximation in the natural functional spaces. The results are not obvious in the first situation. In this case, the well-known conditions for the well posedness and convergence of the corresponding steady problem are not sufficient for the good approximation of the time dependent problem. This issue is demonstrated with a numerical (counter-) example and justified analytically. © 2004 Society for Industrial and Applied Mathematics.

UR - http://epubs.siam.org/doi/10.1137/S0036142903431821

UR - http://www.scopus.com/inward/record.url?scp=25444529958&partnerID=8YFLogxK

U2 - 10.1137/S0036142903431821

DO - 10.1137/S0036142903431821

M3 - Article

VL - 42

SP - 1502

EP - 1526

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

SN - 0036-1429

IS - 4

ER -