[PDF] Top 20 Evolving surface finite element methods for random advection-diffusion equations

... lognormal random fields. Well-posedness for problems with such kind of random coefficients is stated in [15] assuming the existence of a suitable KL ...Gaussian random field which in turn provides ... See full document

... the random ESFEM discretization in the spirit of [16] leading to the precise formulation and well-posedness of our semi discretization in space presented in Sec- tion ... See full document

... a surface. This may be of particular value when the surface partial differential equation is coupled to a bulk system of equations and when the surface is described as a level set function or ... See full document

... ADER finite volume approach computes high-order approximations to the integral averages ...the equations preserve their source terms, if present ...Galerkin finite element methods is ... See full document

... discretization methods for advection-diffusion equations on moving surfaces arise because of the moving ge- ...finite element approximations has been given in [4, ...of advection-diffusion ... See full document

... to advection-dominated ...the Finite Element (FE) context, where stabilized formulations have been developed to deal with the numerical instabilities of the Galerkin ...Navier–Stokes Equations ... See full document

... The surface finite element method for pattern formation on evolving biological surfaces, ...finite element method on a fixed mesh for the Stefan problem with convection in a saturated porous ... See full document

... fractional advection–diffu- sion ...analytical methods are usually required. The finite element method was constructed for the space fractional advection–diffusion equation by Zheng et ...tional ... See full document

... in either of the two equations. But this would alter the positive definiteness. As seen in the subsequent analysis, if (3.1) is written in a nonmixed form (or the standard Galerkin version), the positive ... See full document

... Numerical methods based on standard finite difference (SFD) or finite element dis- cretizations are widely used, see for example ...imply finite difference schemes that are nonstandard ... See full document

... differential equations on time evolving hypersurfaces arise in many applications in biology, fluids and materials science, for example see [6, 7, 13, 14, 17] and the references cited ...parabolic ... See full document

... of advection-diffusion equations on moving two-dimensional surfaces for f = 0 performed in [11] using an evolving surface finite element ...and surface parametrisations, is very ... See full document

... bulk equations in one space dimension ...the surface is computed implicitly using phase field or level set methods or when one wishes to use bulk finite element ...the surface ... See full document

... numerical methods that have been applied to advection-diffusion equation include finite difference me- thods, Galerkin methods, spectral methods, wavelet based finite ... See full document

... bulk equations in one space dimension ...the surface is computed implicitly using phase field or level set methods [4, 32, ...a surface triangulation. One idea is to solve the surface ... See full document

... The analysis is performed for the model problems of linear steady-state and time-dependent convection-diffusion-reaction equations. Applying a nonlinear discretization scheme to a lin- ear problem leads ... See full document

... reaction diffusion equations ...membrane diffusion motivates the use of ordinary differential equations (ODEs) to model the membrane-bound species at the two ... See full document

... finite element case, using a modification of the Oswald interpolation operator, detailed discussions, and further numerical experiments are presented in [24, ... See full document

... N´ed´elec element approxima- tion of the time harmonic Maxwell equations at a prescribed temporal frequency ω on tensor product meshes of size h is ... See full document

... In this paper, we use the lowest Raviart-Thomas rectangle mixed finite element to approx- imate problem (.) and derive the uniform error estimates for the characteristics-mixed finite element schemes. ... See full document