Abstract This article extends the semidiscrete maximal $L^p$-regularity results in Li (2019, Analyticity, regularity and maximum-norm stability of semi-discrete finite element solutions parabolic equations nonconvex polyhedra. Math. Comp., 88, 1--44) to multistep fully discrete methods for with more general diffusion coefficients $W^{1,d+\beta }$, where $d$ is dimension space $\beta>0$. ...

Variational time discretization schemes are getting of increasing importance for the accurate numerical approximation of transient phenomena. The applicability and value of mixed finite element methods in space for simulating transport processes have been demonstrated in a wide class of works. We consider a family of continuous Galerkin-Petrov time discretization schemes that is combined with a...

A stable mixed finite element method (MFEM) for the second order elliptic problems, in which the scheme just satisfies the discrete B.B condition, is discussed in this paper. The uniqueness and existence of solutions for the corresponding discrete problems are obtained, and the optimal O(h) order error estimates are derived.

We show how mixed finite element methods that satisfy the conditions of finite element exterior calculus can be used for the horizontal discretisation of dynamical cores for numerical weather prediction on pseudo-uniform grids. This family of mixed finite element methods can be thought of in the numerical weather prediction context as a generalisation of the popular polygonal C-grid finite diff...

In this paper we prove that finite element discrete harmonic functions with mixed Dirichlet and Neumann boundary conditions satisfy a weak (Agmon-Miranda) maximum principle on convex polygonal domains. Using this result, we establish the stability of the Ritz projection with mixed boundary conditions in L∞ norm up to a logarithmic term.

Modeling shot peening process is very complex as it involves the interaction of metallic surfaces with a large number of shots of very small diameter. Conventionally such problems are solved using the finite element software (such as ABAQUS) to predict the stresses and strains. However, the number of shots involved and the number of elements required in a real-life components for a 100% coverag...

In this paper we analyze the finite element discretization for the first-order system least squares mixed model for the second-order elliptic problem by means of using nonconforming and conforming elements to approximate displacement and stress, respectively. Moreover, on arbitrary regular quadrilaterals, we propose new variants of both the rotated Q1 nonconforming element and the lowest-order ...