Four primal discontinuous Galerkin methods are applied to solve reactive transport problems, namely, Oden-BabuSka-Baumann DG （OBB-DG）, non-symmetric interior penalty Galerkin （NIPG）, symmetric interior penalty Gal...
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Four primal discontinuous Galerkin methods are applied to solve reactive transport problems, namely, Oden-BabuSka-Baumann DG （OBB-DG）, non-symmetric interior penalty Galerkin （NIPG）, symmetric interior penalty Galerkin （SIPG）, and incomplete interior penalty Galerkin （IIPG）. A unified a posteriori residual-type error estimation is derived explicitly for these methods. From the computed solution and given data, explicit estimators can be computed efficiently and directly, which can be used as error indicators for adaptation. Unlike in the reference [10], we obtain the error estimators in L^2 （L^2） norm by using duality techniques instead of in L^2（H^1） norm.
In this paper, we provide a theoretical method（PUFEM）, which belongs to the analysis of the partition of unity finite element family of meshfree methods. The usual error analysis only shows the order of error estima...
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In this paper, we provide a theoretical method（PUFEM）, which belongs to the analysis of the partition of unity finite element family of meshfree methods. The usual error analysis only shows the order of error estimate to the same as the local approximations[12]. Using standard linear finite element base functions as partition of unity and polynomials as local approximation space, in l-d case, we derive optimal order error estimates for PUFEM interpolants. Our analysis show that the error estimate is of one order higher than the local approximations. The interpolation error estimates yield optimal error estimates for PUFEM solutions of elliptic boundary value problems.
We present and analyze a robust preconditioned conjugate gradient method for the higher order Lagrangian finite element systems of a class of elliptic problems. An auxiliary linear element stiffness matrix is chosen t...
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We present and analyze a robust preconditioned conjugate gradient method for the higher order Lagrangian finite element systems of a class of elliptic problems. An auxiliary linear element stiffness matrix is chosen to be the preconditioner for higher order finite elements. Then an algebraic multigrid method of linear finite element is applied for solving the preconditioner. The optimal condition number which is independent of the mesh size is obtained. Numerical experiments confirm the efficiency of the algorithm.
In this paper, we present a novel indirect convergent Jacobi spectral collocation method for fractional optimal control problems governed by a dynamical system including both classical derivative and Caputo fractional...
In this paper, we develop spectral collocation method for a class of fractional diffusion differential equations. Since the solutions of these fractional differential equations usually exhibit singularities at the end...
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In this study, we construct a space-time finite element (FE) scheme and furnish cost-efficient approximations for one-dimensional multi-term time fractional advection diffusion equations on a bounded domain Ω. Firstl...
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