TY - JOUR
T1 - Virtual element methods for the three-field formulation of time-dependent linear poroelasticity
AU - Bürger, Raimund
AU - Kumar, Sarvesh
AU - Mora, David
AU - Ruiz-Baier, Ricardo
AU - Verma, Nitesh
PY - 2021/2
Y1 - 2021/2
N2 - A virtual element discretisation for the numerical approximation of the three-field formulation of linear poroelasticity introduced in R. Oyarzúa and R. Ruiz-Baier, (SIAM J. Numer. Anal.54 2951–2973, 2016) is proposed. The treatment is extended to include also the transient case. Appropriate poroelasticity projector operators are introduced and they assist in deriving energy bounds for the time-dependent discrete problem. Under standard assumptions on the computational domain, optimal a priori error estimates are established. These estimates are valid independently of the values assumed by the dilation modulus and the specific storage coefficient, implying that the formulation is locking-free. Furthermore, the accuracy of the method is verified numerically through a set of computational tests.
AB - A virtual element discretisation for the numerical approximation of the three-field formulation of linear poroelasticity introduced in R. Oyarzúa and R. Ruiz-Baier, (SIAM J. Numer. Anal.54 2951–2973, 2016) is proposed. The treatment is extended to include also the transient case. Appropriate poroelasticity projector operators are introduced and they assist in deriving energy bounds for the time-dependent discrete problem. Under standard assumptions on the computational domain, optimal a priori error estimates are established. These estimates are valid independently of the values assumed by the dilation modulus and the specific storage coefficient, implying that the formulation is locking-free. Furthermore, the accuracy of the method is verified numerically through a set of computational tests.
KW - A priori error analysis
KW - Biot equations
KW - Time-dependent problems
KW - Virtual element method
UR - http://www.scopus.com/inward/record.url?scp=85098666566&partnerID=8YFLogxK
U2 - 10.1007/s10444-020-09826-7
DO - 10.1007/s10444-020-09826-7
M3 - Article
AN - SCOPUS:85098666566
VL - 47
JO - Advances in Computational Mathematics
JF - Advances in Computational Mathematics
SN - 1019-7168
IS - 2
M1 - 2
ER -