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Volume 3, Issue 4
Error Estimates Under Minimal Regularity for Single Step Finite Element Approximations of Parabolic Partial Differential Equations

L. S. Hou & W. Zhu

Int. J. Numer. Anal. Mod., 3 (2006), pp. 504-524.

Published online: 2006-03

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  • Abstract

This paper studies error estimations for a fully discrete, single step finite element scheme for linear parabolic partial differential equations. Convergence in the norm of the solution space is shown and various error estimates in this norm are derived. In contrast to like results in the extant literature, the error estimates are derived in a stronger norm and under minimal regularity assumptions.

  • Keywords

fully discrete approximation, parabolic equations, error estimate, finite element methods, backward Euler method.

  • AMS Subject Headings

65M12, 65M15, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-3-504, author = {L. S. Hou and W. Zhu}, title = {Error Estimates Under Minimal Regularity for Single Step Finite Element Approximations of Parabolic Partial Differential Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2006}, volume = {3}, number = {4}, pages = {504--524}, abstract = {

This paper studies error estimations for a fully discrete, single step finite element scheme for linear parabolic partial differential equations. Convergence in the norm of the solution space is shown and various error estimates in this norm are derived. In contrast to like results in the extant literature, the error estimates are derived in a stronger norm and under minimal regularity assumptions.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/915.html} }
TY - JOUR T1 - Error Estimates Under Minimal Regularity for Single Step Finite Element Approximations of Parabolic Partial Differential Equations AU - L. S. Hou & W. Zhu JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 504 EP - 524 PY - 2006 DA - 2006/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/915.html KW - fully discrete approximation, parabolic equations, error estimate, finite element methods, backward Euler method. AB -

This paper studies error estimations for a fully discrete, single step finite element scheme for linear parabolic partial differential equations. Convergence in the norm of the solution space is shown and various error estimates in this norm are derived. In contrast to like results in the extant literature, the error estimates are derived in a stronger norm and under minimal regularity assumptions.

L. S. Hou and W. Zhu. (2006). Error Estimates Under Minimal Regularity for Single Step Finite Element Approximations of Parabolic Partial Differential Equations. International Journal of Numerical Analysis and Modeling. 3 (4). 504-524. doi:
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