TY - JOUR
T1 - Stability of semidiscrete formulations for parabolic problems at small time steps
AU - Harari, Isaac
PY - 2004/4/16
Y1 - 2004/4/16
N2 - Solutions of direct time-integration schemes that converge in time to conventional semidiscrete formulations may be polluted at small time steps by spurious spatial oscillations, along with attendant overshoot in time. This degradation is not an artifact of the time-marching scheme, but rather a property of the solution of the semidiscrete formulation itself. A critical time step for the onset of spatial oscillations is derived by analogy to singularly perturbed elliptic problems. We then propose a simple procedure of spatial stabilization to remove this pathology from implicit time-integration schemes, without affecting unconditional temporal stability. Spatially stabilized implicit time integration is free of spurious spatial oscillations at small time steps, and numerical experience points to improved temporal accuracy as well.
AB - Solutions of direct time-integration schemes that converge in time to conventional semidiscrete formulations may be polluted at small time steps by spurious spatial oscillations, along with attendant overshoot in time. This degradation is not an artifact of the time-marching scheme, but rather a property of the solution of the semidiscrete formulation itself. A critical time step for the onset of spatial oscillations is derived by analogy to singularly perturbed elliptic problems. We then propose a simple procedure of spatial stabilization to remove this pathology from implicit time-integration schemes, without affecting unconditional temporal stability. Spatially stabilized implicit time integration is free of spurious spatial oscillations at small time steps, and numerical experience points to improved temporal accuracy as well.
KW - Rothe method
KW - Semidiscrete
KW - Small time step oscillation
KW - Spatial stabilization
UR - http://www.scopus.com/inward/record.url?scp=2042455855&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2003.12.035
DO - 10.1016/j.cma.2003.12.035
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AN - SCOPUS:2042455855
SN - 0045-7825
VL - 193
SP - 1491
EP - 1516
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
IS - 15-16
ER -