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View article: ANALYSIS OF FOURTH-ORDER DIFFERENCE APPROXIMATION SCHEMES FOR FRACTIONAL DIFFUSION EQUATIONS
ANALYSIS OF FOURTH-ORDER DIFFERENCE APPROXIMATION SCHEMES FOR FRACTIONAL DIFFUSION EQUATIONS Open
Two fourth-order difference approximations for fractional derivatives based on Lubich-type second-order approximation with different shifts are derived. These approximations are applied to the space fractional diffusion equation with the C…
View article: Equal-order finite element approximation for mantle-melt transport
Equal-order finite element approximation for mantle-melt transport Open
Mantle convection and melt migration are important processes for understanding Earth’s dynamics and how they relate to observations at the surface. Recently it has been established that melt migration can be modelled by coupling variable-v…
View article: Algebraic construction of a third order difference approximations for fractional derivatives and applications
Algebraic construction of a third order difference approximations for fractional derivatives and applications Open
Finite difference approximations for fractional derivatives based on Grunwald formula are well known to be of first order accuracy, but display unstable solutions with known numerical methods. The shifted form of the Grunwald approximation…
View article: A New Second Order Approximation for Fractional Derivatives with Applications
A New Second Order Approximation for Fractional Derivatives with Applications Open
We propose a generalized theory to construct higher order Grünwald type approximations for fractional derivatives. We use this generalization to simplify the proofs of orders for existing approximation forms for the fractional derivative. …
View article: Algebraic construction of higher order difference approximations for fractional derivatives and applications
Algebraic construction of higher order difference approximations for fractional derivatives and applications Open
A generalization of the Grünwald difference approximation for fractional derivatives in terms of a real sequence and its generating function is presented. Properties of the generating function are derived for consistency and order of accur…
View article: Analysis of Subgrid Stabilization Method for Stokes-Darcy Problems
Analysis of Subgrid Stabilization Method for Stokes-Darcy Problems Open
A number of techniques, used as remedy to the instability of the Galerkin finite element formulation for Stokes like problems, are found in the literature. In this work we consider a coupled Stokes-Darcy problem, where in one part of the d…