What question did this study set out to answer?

This research aims to analyze the convergence and superconvergence of an ultra-weak discontinuous Galerkin method for nonlinear Volterra integro-differential equations.

June 29, 2026Numerical AlgorithmsOpen Access

Superconvergence analysis of an ultra-weak discontinuous galerkin method for nonlinear second-order volterra integro-differential equations

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Authors

MBMahboub BaccouchUniversity of Nebraska at Omaha

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Implication

Randomized trial demonstrates superconvergence of an ultra-weak method in nonlinear equations, indicating improved efficiency and accuracy.

Key Points

This research aims to analyze the convergence and superconvergence of an ultra-weak discontinuous Galerkin method for nonlinear Volterra integro-differential equations.
Analysis of the UWDG method's convergence properties
Deriving optimal error estimates in L2 norm using numerical fluxes
Confirmation through numerical experiments on arbitrary regular meshes
Achieved optimal convergence order of p+1 for the UWDG method with piecewise polynomials of degree p ≥ 2
Demonstrated superconvergence of order p+2 toward a projection of the exact solution
Established O(h^2p) superconvergence for UWDG solutions and their derivatives at the end of each time step

Cite This Study

Mahboub Baccouch (2026) studied this question.

synapsesocial.com/papers/6a420b08f91bb43ea9192249 https://doi.org/10.1007/s11075-026-02421-9

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Implication

Randomized trial demonstrates superconvergence of an ultra-weak method in nonlinear equations, indicating improved efficiency and accuracy.

Superconvergence analysis of an ultra-weak discontinuous galerkin method for nonlinear second-order volterra integro-differential equations

Discussion

Member takes

Implication

Key Points

Cite This Study

Superconvergence analysis of an ultra-weak discontinuous galerkin method for nonlinear second-order volterra integro-differential equations

Discussion

Member takes

Implication

Key Points

Cite This Study

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