Superconvergence Analysis and Extrapolation of Quasi-Wilson Nonconforming Finite Element Method for Nonlinear Sobolev Equations

Quasi-Wilson nonconforming finite element approximation for a class of nonlinear Sobolev equa- tions is discussed on rectangular meshes. We first prove that this element has two special characters by novel approaches. One is that （Vh（U -- Ihu）,VhVh）h may be estimated as order O（h2） when u E H3（Ω）, where Iuu denotes the bilinear interpolation of u, vh is a polynomial belongs to quasi-Wilson finite element space and △h denotes the piecewise defined gradient operator, h is the mesh size tending to zero. The other is that the consistency error of this element is of order O（h2）/O（h3） in broken Hi-norm, which is one/two order higher than its interpolation error when u ε Ha（Ω）/H4 （（1）. Then we derive the optimal order error estimate and su- perclose property via mean-value method and the known high accuracy result of bilinear element. Furthermore, we deduce the global superconvergence through interpolation post processing technique. At last, an extrapola- tion result of order O（h3）, two order higher than traditional error estimate, is obtained by constructing a new suitable extrapolation scheme.

EQ^(rot)_1 Nonconforming Finite Element Method for Nonlinear Dual Phase Lagging Heat Conduction Equations

EQrot nonconforming finite element approximation to a class of nonlinear dual phase lagging heat conduction equations is discussed for semi-discrete and fully-discrete schemes. By use of a special property, that is, the consistency error of this element is of order O（h2） one order higher than its interpolation error O（h）, the superclose results of order O（h2） in broken Hi-norm are obtained. At the same time, the global superconvergence in broken Hi-norm is deduced by interpolation postprocessing technique. Moreover, the extrapolation result with order O（h4） is derived by constructing a new interpolation postprocessing operator and extrapolation scheme based on the known asymptotic expansion formulas of EQrot element. Finally, optimal error estimate is gained for a proposed fully-discrete scheme by different approaches from the previous literature.

High Accuracy Analysis of the Lowest Order H1-Galerkin Mixed Finite Element Method for Nonlinear Sine-Gordon Equations

The lowest order H1-Galerkin mixed finite element method （for short MFEM） is proposed for a class of nonlinear sine-Gordon equations with the simplest bilinear rectangular element and zero order Raviart- Thomas element. Base on the interpolation operator instead of the traditional Ritz projection operator which is an indispensable tool in the traditional FEM analysis, together with mean-value technique and high accuracy analysis, the superclose properties of order O（h2）/O（h2 ＋ r2） in Hi-norm and H（div; Ω）-norm axe deduced for the semi-discrete and the fully-discrete schemes, where h, r- denote the mesh size and the time step, respectively, which improve the results in the previous literature.

Spatial High Accuracy Analysis of FEM for Two-dimensional Multi-term Time-fractional Diffusion-wave Equations

In this paper, high-order numerical analysis of finite element method（FEM） is presented for twodimensional multi-term time-fractional diffusion-wave equation（TFDWE）. First of all, a fully-discrete approximate scheme for multi-term TFDWE is established, which is based on bilinear FEM in spatial direction and Crank-Nicolson approximation in temporal direction, respectively. Then the proposed scheme is proved to be unconditionally stable and convergent. And then, rigorous proofs are given here for superclose properties in H-1-norm and temporal convergence in L-2-norm with order O（h-2＋ τ-（3-α））, where h and τ are the spatial size and time step, respectively. At the same time, theoretical analysis of global superconvergence in H-1-norm is derived by interpolation postprocessing technique. At last, numerical example is provided to demonstrate the theoretical analysis.

Successful treatment of early onset Epstein-Barr virus-negative T-cell lymphoproliferative disorder after allogeneic hematopoietic stem cell transplantation with histone deacetylase inhibitor chidamide

To the Editor:A 58-year-old man,who diagnosed with chronic myelomonocytic leukemia in June 2019,achieved complete bone marrow remission after five courses of chemotherapy(decitabine 35 mg,days 1–5).In December 2019,he underwent an allogeneic hematopoietic stem cell transplant(allo-HSCT)from his human leukocyte antigen-haploidentical daughter.The donor and host pre-trans-plant Epstein-Barr virus(EBV)serologies were negative.The myeloablative conditioning regimen was administered with cytarabine,busulfan,cyclophosphamide,methyl-N-(2-chloroethyl)-N-cyclohexyl-N-nitrosourea,and anti-thy-mocyte globulin.The numbers of mononuclear cells and CD34+cells were 12.23108/kg and 7.57108/kg,respectively.Graft-versus-host disease(GVHD)prophy-laxis included cyclosporin A(CSA)and mycophenolate mofetil(MMF).CSA was later changed to tacrolimus due to a gastrointestinal reaction on day+15.The patient had a history of tuberculosis(TB)and received isoniazid and rifapentine for prevention.Neutrophil and platelet engraftment occurred on day+12 and+18,respectively.Cytogenetic studies showed complete donor chimerism on day+26.

Colon carcinoma treated with oxaliplatin and capecitabine in a 12-year-old child

Background:XELOX(oxaliplatin 130mg/m^(2)iv,capecitabine 1000mg/m^(2)bid oral d1–14,q3w)chemotherapy has never been used in children.In this report,we present a case of a 12-year-old girl with colon adenocarcinoma,treated with surgery and XELOX chemotherapy.Methods:On admission,the girl complained of abdominal pain and intestinal obstruction.Physical examination revealed a distended abdomen with tenderness on the left upper quadrant.Barium enema revealed a stenotic lesion at the distal end of the transverse colon,and abdominal computed tomography showed acute obstruction and a colonic mass.Laparotomy was performed after the failure of conservative treatment.Results:The mass was originated from the transverse colon.Frozen sections of the specimens revealed an adenocarcinoma.Transverse colectomy was performed and regional lymph nodes were removed.Pathological examination confirmed that the mass was a poorly differentiated adenocarcinoma,and XELOX chemotherapy was used.No evidence of recurrent or metastatic tumor was found after 18 months.Conclusion:Although complete resection is the most effective treatment,XELOX chemotherapy is beneficial to the improvement of clinical outcome of patients with colon adenocarcinoma.