Unifying a posteriori error analysis of five piecewise quadratic discretisations for the biharmonic equation
An abstract property (H) is the key to a complete a priori error analysis in the (discrete) energy norm for several nonstandard finite element methods in the recent work [Lowest-order equivalent nonstandard finite element methods for biharmonic plates, Carstensen and Nataraj, M2AN, 2022]. This paper...
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| creator | Carstensen, Carsten Gräßle, Benedikt Nataraj, Neela |
| description | An abstract property (H) is the key to a complete a priori error analysis in
the (discrete) energy norm for several nonstandard finite element methods in
the recent work [Lowest-order equivalent nonstandard finite element methods for
biharmonic plates, Carstensen and Nataraj, M2AN, 2022]. This paper investigates
the impact of (H) to the a posteriori error analysis and establishes known and
novel explicit residual-based a posteriori error estimates. The abstract
framework applies to Morley, two versions of discontinuous Galerkin, $C^0$
interior penalty, as well as weakly over-penalized symmetric interior penalty
schemes for the biharmonic equation with a general source term in
$H^{-2}(\Omega)$. |
| doi_str_mv | 10.48550/arxiv.2310.05648 |
| format | Article |
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the (discrete) energy norm for several nonstandard finite element methods in
the recent work [Lowest-order equivalent nonstandard finite element methods for
biharmonic plates, Carstensen and Nataraj, M2AN, 2022]. This paper investigates
the impact of (H) to the a posteriori error analysis and establishes known and
novel explicit residual-based a posteriori error estimates. The abstract
framework applies to Morley, two versions of discontinuous Galerkin, $C^0$
interior penalty, as well as weakly over-penalized symmetric interior penalty
schemes for the biharmonic equation with a general source term in
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the (discrete) energy norm for several nonstandard finite element methods in
the recent work [Lowest-order equivalent nonstandard finite element methods for
biharmonic plates, Carstensen and Nataraj, M2AN, 2022]. This paper investigates
the impact of (H) to the a posteriori error analysis and establishes known and
novel explicit residual-based a posteriori error estimates. The abstract
framework applies to Morley, two versions of discontinuous Galerkin, $C^0$
interior penalty, as well as weakly over-penalized symmetric interior penalty
schemes for the biharmonic equation with a general source term in
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the (discrete) energy norm for several nonstandard finite element methods in
the recent work [Lowest-order equivalent nonstandard finite element methods for
biharmonic plates, Carstensen and Nataraj, M2AN, 2022]. This paper investigates
the impact of (H) to the a posteriori error analysis and establishes known and
novel explicit residual-based a posteriori error estimates. The abstract
framework applies to Morley, two versions of discontinuous Galerkin, $C^0$
interior penalty, as well as weakly over-penalized symmetric interior penalty
schemes for the biharmonic equation with a general source term in
$H^{-2}(\Omega)$.</abstract><doi>10.48550/arxiv.2310.05648</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Numerical Analysis Mathematics - Numerical Analysis |
| title | Unifying a posteriori error analysis of five piecewise quadratic discretisations for the biharmonic equation |
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