TY - JOUR
T1 - Pointwise-in-time a posteriori error control for time-fractional parabolic equations
AU - Kopteva, Natalia
N1 - Publisher Copyright:
© 2021 The Author(s)
PY - 2022/1
Y1 - 2022/1
N2 - For time-fractional parabolic equations with a Caputo time derivative of order α∈(0,1), we give pointwise-in-time a posteriori error bounds in the spatial L2 and L∞ norms. Hence, an adaptive mesh construction algorithm is applied for the L1 method, which yields optimal convergence rates 2−α in the presence of solution singularities.
AB - For time-fractional parabolic equations with a Caputo time derivative of order α∈(0,1), we give pointwise-in-time a posteriori error bounds in the spatial L2 and L∞ norms. Hence, an adaptive mesh construction algorithm is applied for the L1 method, which yields optimal convergence rates 2−α in the presence of solution singularities.
KW - Fractional-order parabolic equation
KW - Graded meshes
KW - L1 scheme
KW - Optimal convergence rates
KW - Pointwise-in-time a posteriori error bounds
UR - http://www.scopus.com/inward/record.url?scp=85112720383&partnerID=8YFLogxK
U2 - 10.1016/j.aml.2021.107515
DO - 10.1016/j.aml.2021.107515
M3 - Article
AN - SCOPUS:85112720383
SN - 0893-9659
VL - 123
JO - Applied Mathematics Letters
JF - Applied Mathematics Letters
M1 - 107515
ER -