An \(h-p\) version of the continuous Petrov-Galerkin finite element method for nonlinear Volterra integro-differential equations. (English) Zbl 1327.65147
Summary: We present an \(h-p\) version of the continuous Petrov-Galerkin finite element method for nonlinear Volterra integro-differential equations. We derive a priori error bounds in the \(L^2\)- and \(H^1\)-norm that are explicit in the time steps, the approximation orders, and the regularity of the exact solution. Numerical experiments are provided to illustrate the theoretical results.
MSC:
| 65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65R20 | Numerical methods for integral equations |
| 65L70 | Error bounds for numerical methods for ordinary differential equations |
Keywords:
nonlinear Volterra integro-differential equations; \(h-p\) version; finite element method; Petrov-Galerkin method; error analysisReferences:
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