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Volume 12, Issue 2
An Adaptive Linear Time Stepping Algorithm for Second-Order Linear Evolution Problems

Junjiang Lai & Jianguo Huang

Int. J. Numer. Anal. Mod., 12 (2015), pp. 230-253.

Published online: 2015-12

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  • Abstract

In this paper, we propose and analyze a linear time stepping finite element method for abstract second order linear evolution problems. For such methods, we derive optimal order a posteriori error estimates and sharp a posteriori nodal error estimates using the energy approach and the duality argument. Based on these estimates, we further design an adaptive time stepping strategy for the previous discretization in time. Several numerical experiments are provided to show the reliability and efficiency of the a-posteriori error estimates and to assess the effectiveness of the proposed adaptive time stepping method.

  • Keywords

A posteriori error analysis, adaptive algorithm, linear finite element, evolution problems.

  • AMS Subject Headings

65M60, 65M15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-12-230, author = {Junjiang Lai and Jianguo Huang}, title = {An Adaptive Linear Time Stepping Algorithm for Second-Order Linear Evolution Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2015}, volume = {12}, number = {2}, pages = {230--253}, abstract = {

In this paper, we propose and analyze a linear time stepping finite element method for abstract second order linear evolution problems. For such methods, we derive optimal order a posteriori error estimates and sharp a posteriori nodal error estimates using the energy approach and the duality argument. Based on these estimates, we further design an adaptive time stepping strategy for the previous discretization in time. Several numerical experiments are provided to show the reliability and efficiency of the a-posteriori error estimates and to assess the effectiveness of the proposed adaptive time stepping method.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/486.html} }
TY - JOUR T1 - An Adaptive Linear Time Stepping Algorithm for Second-Order Linear Evolution Problems AU - Junjiang Lai & Jianguo Huang JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 230 EP - 253 PY - 2015 DA - 2015/12 SN - 12 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/486.html KW - A posteriori error analysis, adaptive algorithm, linear finite element, evolution problems. AB -

In this paper, we propose and analyze a linear time stepping finite element method for abstract second order linear evolution problems. For such methods, we derive optimal order a posteriori error estimates and sharp a posteriori nodal error estimates using the energy approach and the duality argument. Based on these estimates, we further design an adaptive time stepping strategy for the previous discretization in time. Several numerical experiments are provided to show the reliability and efficiency of the a-posteriori error estimates and to assess the effectiveness of the proposed adaptive time stepping method.

Junjiang Lai and Jianguo Huang. (2015). An Adaptive Linear Time Stepping Algorithm for Second-Order Linear Evolution Problems. International Journal of Numerical Analysis and Modeling. 12 (2). 230-253. doi:
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