RT Journal Article
T1 Convolution quadrature for the quasilinear subdiffusion equation.
A1 López-Fernández, María
A1 Plociniczak, Lukasz
K1 Ecuaciones en derivadas parciales
K1 Análisis matemático
AB We construct a convolution quadrature (CQ) scheme for the quasilinear subdiffusion equation of order a and supply it with the fast and oblivious implementation. In particular, we find a condition for the CQ to be admissible and discretize the spatial part of the equation with the finite element method. We prove the unconditional stability and convergence of the scheme and find a bound on the error. Our estimates are globally optimal for all 0 <a <1 and pointwise for a ≥1/2 in the sense that they reduce to the well-known results for the linear equation. For the semilinear case, our estimates are optimal both globally and locally. As a passing result, we also obtain a discrete Grönwall inequality for the CQ, which is a crucial ingredient in our convergence proof based on the energy method. The paper concludes with numerical examples verifying convergence and computation time reduction when using fast and oblivious quadrature.
PB Society for Industrial and Applied Mathematics (SIAM)
YR 2025
FD 2025-07-15
LK https://hdl.handle.net/10630/41466
UL https://hdl.handle.net/10630/41466
LA eng
NO Convolution Quadrature for the Quasilinear Subdiffusion Equation Maria López-Fernández and Łukasz Płociniczak, SIAM Journal on Numerical Analysis 2025, 63:4, 1482-1511
NO https://openpolicyfinder.jisc.ac.uk/id/publication/13598?from=single_hit
NO Fundación BBVA
NO Ministerio de Ciencia, Innovación y Universidades
NO Universidad de Malaga
NO National Science Centre, Poland
NO Beca Leonardo for Researchers and Cultural Creators 2022
NO Proyecto 16 - proyecto G Plan Propio
NO PID2022-137637NB-C21
NO NCN 2020/38/E/ST1/00153
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 22 ene 2026